WE CLAIM: 1. A compound of formula (I) or a stereoisomer, internal salt, N-oxide, prodrug, or pharmaceutically acceptable salt thereof: wherein: A represents -NR°R or -ORz;' Z represents -H or -CH3; X represents -S- or -CHj-; Rz represents isoxazolyl; R° is hydrogen or Ci^alkyl which is optionally substituted with one or two substituents selected from halogen, hydroxyl, cyano, carbamoyl, -SO2NH2 and Ci-6alkoxy; R is: 1) ■ -(CH2)nC(=0)R2, 2) _(CH2)nC(=S)R2, 3) -(CH2)DS02R2, . 4) -Ci^alkyl optionally substituted with -C3^cycloalkyl, or 5) -CH(=NH),or R and R together with the N to which they are attached form a substituted or unsubstituted 5r6' membered cyclic ring with 0, 1, 2, 3 or 4 additional beteroatom ring atoms independently selected from N, 0 and S; n is an integer selected from 0, 1, 2, 3, 4, 5 and 6; R1 is: 1) -CCHWw-AiyC, 3) - 39) -(CH2)o.2triazolyl optionally substituted with -CH2NH2, and 40) -(CH2)o-2tetrazolyl; Rf is H, -C(=0)N(Cwalky!)2, -S02Cwalkyl, -nS02N(R*)2, -C(=0)-cyclopentyl-N(Rx)2> -C(=0)-pyridinyl optionally substituted with one or more groups selected from oxo, -Ci-3alkyl and -OH, -C(=OH>yrrolidinyVsubstituted with -NRBRb or halogen, -C(=0)-thiazolidinyl>.-SO2-piperazine, or -SOr-pyrrolidinyl-N(Rx)2; RE is hydrogen or Cualkyl, or Rf and R8 are taken together, with the N to which they are attached, to form morpholinyl; piperazinyl; pyrrolidiny! optionally substituted with -CH3;. piperidinyl or thiomorpholinyl optionally substituted with -G.6alkyl or -N(TRX)2; or triazolyl substituted with -CH2MH2; Rh and-Rj is independently H, Chalky], or Cj-gcycloalkyl; R1 is -Ci-s amino alky!, -OQ^alkyl, -Cucyanoalkyl, or-Ci^haloalkyl optionally substituted with -NRxRy; Rk is Ci^alkyl, or thiazole substituted with -NH2; each R* and Ry is independently hydrogen or Ci-3alkyl; and wherein when HetA, AryA, AryC, HetC, or the rings formed by combining R and R° are substituted, the substituents are 1 to 4 members selected from 1) halogen, 2) -OH, 3) oxo, 4) -COOH, 5) -COpCi-salkyi, 6) C^aUcyl, - 7) Ci^alkoxy, 8) -CCHOo-aO-Cijalkyl, 9) Ci^haloalkyl, ■ 10) Cuhydroxyalkyl, 11) C3-C8cycloalkyl, 12) -C(=0)Ci-fialkyl, ■13) -C(=0)Ci-6aminoalkyl, 14) -C(=0)NRcRd; 15) -(CH2)o-iNR,[R5', ' 16) -iRcRd> 22) -CH=NH, 23) -CCH2y3C(=NH)NH2, 24) - -NRxRy, -NHS02NRIRy, -S02NReRdJ thiazolyl, and 4,5-dihydrothiazol-2-yl. 9. The compound of any one of claims 1 to 8, or a stereoisomer, internal salt, N-oxide, or pharmaceutically acceptable salt thereof, wherein Rcis- 'OH,. 2) -CH2CN, 3) -Chalky! optionally substituted with -NRhRJ, pyrrolidinyl or -OH, 4) -CH2CH2C(=0)NRxRy, 5)- -CH2CH2C(=0)NHCH2CH2OH, 6) -CH2CH2C(=0)NHOCH3, ' 7) -CH2CH2C(=0)NHOBn, 8) -Ci.6alkoxy, 9) pyridinyl, 10) pyrrolidinyl .optionally substituted with -C(=0)NRxRy, 11) -~C(=NH)-pyrrolidin-1 -yl optionally substituted with NRxRy 12) tetrahydro-2H-pyran-4-yl, 13) -CH2CH2C(=0)-diazepanyl, 14) -CH2CH2C(=0)-pyrrolidin-l-yl substituted with NR*Ry, 15) -CHj-pyrany! optionally substituted with 1 or 2 substituerits selected from oxo and methoxy, 16) -CH2-pyridinyl optionally substituted with -CH3, -OH, and oxo, 17) -phenyl-C(=0)-piperazinyl, 18) -phenyl-CH2-NRxRy, or 19) -i)henyl-C(=0>-pyrrolidinyl-NR!'Ry; Rd is hydrogen, or Ci-3alkyl; or Rc and Rd are taken together, with the N to which they are attached, to form a) a 4- to 8-membered heterocyclic ring with 0, 1, or 2 additional heteroatom ring atoms independently selected from N, O, and S, or b) a 6- to 12-membered heterocyclic bi- or tricyclic ring with 0,1, or 2 additional heteroatom ring atoms independently selected from N, O, and S, wherein the bicyclic ring is , optionally bridged, fused, spirocyclic or any combination of two thereof, and wherein any nitrogen ring atom of the heterocyclic ring or heterocyclic bicyclic ring is optionally quadricbvalent; and wherein the heterocyclic ring or heterocyclic bicyclic ring is optionally substituted with 1, 2 or 3 substituents independently selected from 38) halogen, 39) • -Ci-ialkyl optionally substituted with 1 or 2 substituents selected from halogen, -CN and -OH, 40) -C(=MH)NH2, 41) -{CH2)0.2C(=O)(CH2)0.2NRhRi optionally substituted with -NH2 or -OH, 42) -{CH2)o-3NRhRi optionally substituted with-NH2 or halogens, 43) -C(=0)Ci^aminoalkyl optionally substituted with -OH, 44) -C(=0)OH, 45) -C(=0)(CH2)o.3NHC(=NH)NH2, ■ 46) -(CH2)o-iNHCH2CH2NRhRj, 47) --pyrrolidinyl optionally substituted with-NH2, 69) azetidinyl optionally substituted with -CH2NH2, -NH2, or -OH, 70) pyrrolidinyl optionally substituted with -NH2, 71) -NHCH2-pyridinyl substituted with oxo, -CHj, and -OH, 72) -NH-pyrimidinyl, 73) triazolyl optionally substituted with -CH2NH2, and 74) tetrazolyl. 10. The compound of claim 1, or a stereoisomer, internal salt, N-oxide, or pharmaceutically acceptable salt thereof, wherein R° is hydrogen and R is: 1) -C(=0)CHF2, 2) -C(=0)CF3, 3) -C(=0)CH2CF3, 4) -C(=0)CF2CF3, 5) -C(=0)CF2-Ci.6alkyl, 6) -C(=0)CHFCH3, 7) -C(=0)CF2CH2NH2, 8) -C(=0)CF2CH2OH, 9) -C(=0)CH2OH, . 10) -C(=0)CH2OCOCH3j 11) -C(=0)CH2CN, 12) -CC^OJCHzSCbCi-ealkyl, 13) -C(=0)CH2SCHF2j 14) -C(=0)CH2S(=0)CHF2, . 15) -C(=0)CH2P(=0)(OCH3)2, I 16) -C(=0)CH2S-tetrazole optionally substituted with-CH3, 17) -^(=0)CHr-thienyl, . 18) -C(=0)CHCNH2)CH2-Ttetra20le, 19) ^(=0)CHCNH2)CH2-pyrazole, 20) -C(=0)CHr-tetrazole optionally substituted with -C(CH3)3j -CF3, -CHF2j ! -CH3lNH2-COOCi^alkyl,thienyl5-CH2NHCH3,-NH2lor-COOEt, 21) -C(=0)CHr-triazoleoptionaIly substituted with--CH2NRaRb, or-CH3 and . -CF3, or -CF3 and -NH2, 22) -C(=0)CH2-^xadiazole-CH2NR1'Rb, 23) -C(=0)C(CH3)2-tetra2ole, ) 24) -C(=0)CH2-azetidine, 25) -C(=0)CH(CH3)-azetidine optionally substituted with oxo, hydroxyethyl, or both, - 26) -C(=0)CHr~pyrrolidinyl optionally substituted with one or more -For-CH2NHCH3, > 27) -Ct^CFr-thienyl, 28) -CXOH^alkyl-NR-R15, 29) -C(=0)-pyrrolidinyl optionally substituted with F or NH2, 30) -C(=0)-tetrahydrofuran, 31) -C(=0)-(CH2)o.ipiperazine) 32) -C(=0)-pyTzrint, 33) -C(=0)-thiazolidine optionally substituted with one or more oxo, 34) -C(=0)-pyrazole optionally substituted with CH3 and CF3, 35) -C(=0)CH(NH2)Ci.6alkyl optionally substituted with -QH or phenyl, ■ 36) -C(=0)CHFC,^alkyl, 37) -C(=0)CH(OH)Ci-6alkyl, 38) -C(=0)CRk=NOC(CH3)2COOHJ 39) -C(=0)CRk=NOCH3; 40) -C(=S)OCi.6alkyl, 41) -C(=0)C(=0)OH, ■ 42) -C(=0)C(=0)NRBRb, ' 43) -C(=0)(CH2)1^C(=0)NRaRb, 44) -C(=0)C(=0)ONRaRb, 45) . -C(=0)C(=0)OC^alkyl, 46) -(CH2)MC(=0)OH, 47) -(CH2)MC(=0)OCMalky, 48) -CCHJ)MCC=0)CCHJ)WOH, 49) -(CH2)wC(=0)(CH2),_6OC1,6alkyl) 50) -C(=0)OCH2CHF2, 51) -C(=0)OCH2CF3, 52) -C(=0)-C3^cycloalkyl substituted with CF3 or NH2> 53) -C].6alkyl-NRBRb, 54) ^Ci-ealkyl- C3-6cycloalkyl, 55) -CCH2)MS02(CH2)(MRe, - 56) -CH(=NH),or 57) -Ci^alkyl, or R and R° together with the N to which they are attached form a (1,2,3-]triazole optionally substituted with -CH2OH, -CH2OCH3j -CH2F, -CH2NH2, -CH2NHCH3, -C(=0)OCH3l or a tetrazole optionally substituted with -NH2. 11. The compound of claim 1, or a stereoisomer, internal salt, N-oxide, or pharmaceutically acceptable salt thereof, wherein R° is hydrogen and R is: 1) -C(=0)CHF2, 2) -C(=0)CH2NH2j 3) -C(=0)CH2NHCH3, 4) -C(=0)CH2NHC(=NH)NH2; 5) -CC^CTHetrazolyl, or 6) . -S02CH3, or R and R° combine together to form -triazolyl optionally substituted with -CH2-OH. 12. The compound of claim 1, or a stereoisomer, internal salt, N-oxide, or ' pharmaceutically acceptable salt thereof, wherein R1 is: 1) pyrrolidinyl substituted,with 1 or 2 of a) -CONR^, ' b) -CON(CH3)CH2CH2C(=0)-pyrrolidin-l-yl substituted with NH2 or diazepanyl, c) -CH2NRfRs, d) -CH=NH, e) F, f) -(CH2)wNHC(=NH)NH2, g) -CH2NHS02-pyrrolidinyl-NH2) h) -CH2NH(C=0>-pyrrolidmyl substituted NH2 or F,. i) -CH2NH(O0>-pyridinyl substituted with oxo, CH3 and OH, j) -CH2NH(C=0)-cyclopentyl-NH2, k) -CH2NHS02-piperazine, 1) -CH3, or . m) OH, 2) ^ , 3) -CHriJyridinyl, 4) thiazole substituted withpyridinyl wherein the pyridinyl is optionally substituted with ■ -CH3or-CH2C(=0)NH2j 5) azeudinyl substituted with-C(=NH)NH2,-S02NH2j thiazolyl or 4,5-dihydrothiazol-2- 6) -CH2CH2-pyridinyl substituted with oxo, CH2NH2 and OH, 7) -CHriJyrrolidinyl substituted with acetyl and -NH2, or -NHS02NH2, 8) -CH2-piperazuie, 9) -CH2CH2~NH(=NH)NH2, 10) U0 11) pyrazole optionally quatemized with-CHb and optionally substituted with -CH2 pyrrolidine, or CH2 piperidine optionally quatemized with -CH3 and optionally substituted with-CH2CH2NH2, 12) -CHy-phenyl substituted with pyrazole optionally quatemized with -CH3 and substituted with-{CHb^NHb, or 13) -CH2CH2NHC02-rer*-butyl. 13. The compound of claim 1, or a stereoisomer, internal salt, N-oxide, or pharmaceutical^ acceptable salt thereof, wherein R1 is pyrrolidinyl substituted with 1) -C(=G)KRcRd; 2) -CH2NHSQ2NH2, or 3) -CH2-pyrrolidinyl-NH23 or 4) -CH2-CO:pyrrolidinyl-NH2; wherein Re is -CH3, Rdis-CH3; • . Rc and Rd are taken together, with the N to which they are attached, to form 1) azetidinyl optionally substituted with-NHC(=NH)NH2, 2) pyrrolidinyl substituted with a. one or two -NH2, b. .-NHCH3, c. -C(Me)2NH2, d. one or two -OH, e. -CH2NH2, f -NHC(=0)CH2NH2, g. -NHG(=0)CH2 CH2NH2, h. -NHC(=0)CH2 NH(=NH)NH2, i. -NHCH=NH, j. -Fand-NEb, k. -NHiand-OH, 1. -NH2and-CH3, m. -NH2 and -CH20H, n. -NH2 and-CH2NH2, 0. -NH2 and-OMe, ■ p. -OHand-CH2NH2. q. -CH2OH and-CH2NH2, r. -NH2 and-COOH, s. -NHC(=NH)NH23 t. -NHC(=NH)NH2 and -OH, u. -NHC(=NH)NH2and-CH20H, v. -NHC(=NH)NH2 and--NH2, w. -NH2 and -CH2NHSO2NH2, x. -CH2FandNH2, y. -OH, -NH2 and -CH2NH2, 2. -OH,-NH2and-CH2OH, or aa. triazolyl substituted with -CH2NH2l 3) piperidinyl substituted with-{CH2)o-2NH25-CH2NHCH2C(=0)NH2,-CH2CH2NH2, -CH3 and -NH2, -CH2OH and. -CH2NH2, -F and -NH2, -OH and -NH2, -CONHCH2CH(OH)CH2NH2j or azetidinyl substituted with -OH or piperazinyl, 4) piperazinyl optionally substituted with one or two-CH3,-CH2NH2,-CH2CH2NH2, -C(=NH)NH2l -CH2CH2NHC(=NH)NH2l _C(=0)(CH2)!.2NH2j -t(=0)CH(NH2)NH2, -CH2CH(NH2)CH2NH2, -CH2CH(F)CH2NH2, -C(=0)CH2NHCH3, -C(=0)CH(NH2)CH2OH,' or -CH3 and -CH2C(=0)NH2; 5) morpholinyl optionally substituted with -rCH2NH2; 6) 1,4-diazepane optionally substituted with -C(=NH)NH2; 7)' octahydro-lH-pyrrolo|3,2-c]pyridine optionally substituted with -CH2CH2NH2,-CH2CH(OH)NH2, or-C(=NH)NH2> 8) . octahydrocycIopenta[c]pyrrole optionally substituted with a. one or two -NH2, b. -NH2and-CH2OH, c. -NH2 and-CHtNHz, d. -NH2, e. -NHC(=NH)NH2, f. ~NHC(-MH)NH2and-CH2OH3or g. s-OH,-NH2and-CH2OH, 9) octahydro-lH-pyrrolol^jS-clpyridine, 10) octahydro- lH-pyrrolo[3,2-c]pyridine optionally substituted with -CH2CH(OH)CH2NH2, . li)octahydro-lH-pyrTOlo[3,4-b]pyridine optionally substituted with -CH2OH, 12) octahydropyrrolo[3,4-b]pyrrole optiooally substituted with -CH2OH, --CHJCHZNHJ, or-C(=NH)NH2; 13) octahydro-lH-pyrrolo[3,4-c]pyridine optiooally substituted with-CHjOH, or-COOH 14) 5,5-dimethyloctahydro-lH-pyrro!o[3,2-c]pyridin-l—5-ium, 15) octahydropyrrolo[3,4-c]pyrrole optionally substituted with-CH2OH, 16) octahydropyrrolo[3,4-d]imidazole optionally substituted with =NH, 17) octahydro-lH-pyrrolotS^-bJpyridine, 18) octahydropynolo[3,4-b][l,4]oxaziiie, 19) 3,6-diazabicyclo[3.2.0]heptane, 20) l,9-diazaspiro[5.5]undecane, 21) decabydro-l,6-naphthyridine, ' 22) 5,6/7,8-tetrahydrbimJdazo[l,5-a]pyrazioe optinally substituted with - NH2) 23) 2,7-diazaspiro[4.4]nonane, 24) 2,8-diazaspiro[4.5]decane, , - 25) 2,6-diazaspiro[3.4]octane, 26) l,7-diazaspiro[3.5]nonane, 27) 2,7-diazaspiro[3.5]nonane, 28) l,8-diazaspiro[4.5]decane," 29) l,7-diazaspiro[4.5]decane, 30) 5-oxa-2-azaspiro[3.4]octane optiooally substituted with -NH2," 31) 3,8-diaza-tricyclo[5.2.1.01,5]decane, or 32) 8-azaspixo[bicyclo[3.2.1]octane-3)3'-pyrrolidine. 14.. The compound of claim 1, or a pharmaceutically acceptable salt thereof, wherein said compound has a structure according to formula la: ■ ' wherein: A is NR°R or -triazolyl substituted with -CH2OH; Ris: 1) ^Cf^^^alkyl-NR8^; . 2) -C(=0)CHF2, ' 3) • -C(=0)CH2SCHF2, 4) -C(-0)CH2NH(CH2)20Me, 5) -C(=0)CH2pyn-olidin, 6) -€{=0)CH2azetidine, 7) -C(=0)CH2piperazine, 8) -C(=0)CH2 pyrrolidine optionally substituted with 1 or 2 substituents selected from fluorine and -CH2NHMe, 9) -CfFCOCHr-tetrazole optionally substituted with -C(CH3)3, -CF3, -CHF2, -CH3, -NHr-COOCi-ealkyl, thienyl, -CH2NHCH3, -NH2, or -COOCH2CH3, or 10) -SC^CHs; . ' . R°isH; ■ '• " ' R'is 1) pyrrolidinyl substituted with 1 or 2 of-CONRcRd, 2) -<:H2NHS02NH2, or 3) -CH2-pyrrolidinyl optionally substituted with -NH2; Ra and Rb are independently H, -C]-6alkyl, -C3.gcycloalkyl, -SQ.CH3, . -CH(=NH), -C(=NH)NH2, or -CH2C(=0)NB2; RcandRd are independently H, Cualkyl, -C(=NH)-pyrrolidinyl optionally substituted with -NH2, or RcandRd are taken together, with the N to which they are attached, to form a 4- to 12-membered heterocyclic ring or.ring system with 0, 1, 2 or 3 additional heteroatom ring atoms selected from N and O; wherein any nitrogen ring atom of the heterocyclic ring or ring system is optionally quadricovalent; the ring system is a bridged, fused or spiro ring system; and the 4- to 12-membered heterocyclic ring or ring system is optionally, substituted with 1, 2 or 3 substituents selected from 1) =NH, 2). -C(=0)(CH2),.2NH2, ■ ■ 3) -C(=0)CH2NHCH3, 4) -CH2CH(NH2)CH2NH2, 5) -C(=0)CH(NH2)CH2NH2, 6) -C(=0)CH(F)CH2NH2) 7) -C(=0)CH(NH2)CH2OH, 8) -CH2CH(OB)CH2NH2, 9) -C(=0)NHCH2CH(OH)CH2NH2l 10) -C(=NH)NH2> 11) -COOH, 12) -Ofe, 13) -CH2C(=0)NH2, 14) -CH2NH CH2C(=0)NH2j 15) . -CH1NRhR.j, 16) -CH2CH2NH2, 17) -CH2CH2NH-C(=NH)-NH2, 18) -C^NHSCbNHi; 19) -CH2OH, 20) - -C(CH3)2NH2, 21) -CH2F; 22) -OH, 23) -OMe, 24) -F, 25) -NRhRj, 26) -NHCH=NH, ■ 27) . -NH-C(=NH)-NH2j 28) -KHCOCH2-NH-C(=NH)-NH2, 29) -NHCOCH2NH2; 30) -(CH2)o.3NRhRj optionally substituted with -NH2 or halogens, 31) azetidinyl optionally substituted with -OH, 32) piperazinyl, and ,33) triazolyl substituted with CH2NH2; and Rh and Rj are independently H, C^aUcyl, or C3.gcycloalkyl. or a stereoisomer, internal salt, N-oxide, prodrug, or phannaceutically acceptable salt thereof. 19. The compound of claim' 1, or a stereoisomer, internal salt, N-oxide, or phannaceutically acceptable salt thereof, wherein Ris-(CH2)nC(=0)R2J-CCH2)nC(=S)R2,-CCH2)„S02K.2, or ^CH(=NH); or R and R° together with N to which they are attached form a substituted or unsubstituted 5-6 membered cyclic ring with 0, 1, 2, 3 or 4 additional heteroatom ring atoms independently selected from N, O and S; with the provisos that when R is -(CH2)DC(=0)R2, n is 0 and R° is H, then R2 is not unsubstituted Ci^alkyl; when R is -fCH2)BC(=0)R2 and n is not 0, R2 is not OH or NH2; when R is -(CH2jnS02R2 and n is not 6, R2 is not OH; and when R and R° combine together to form triazole then Z is not H. 20. - The compound of claim 1, or a stereoisomer, internal salt, N- oxide, or pharmaceutically acceptable salt thereof, wherein R1 is C^aminoalkyl optionally substituted with -CR^NR*. 21. The compound of claim 1 wherein said pharmaceutically acceptahle salt is selected from sodium, potassium, calcium, magnesium and ammonium salts. 22. A pharmaceutical composition which comprises a compound according to any one of claims 1 to 18, or a pharmaceutically acceptahle salt thereof, and a pharmaceutically acceptable carrier. 23. A method for treating a bacterial infection which comprises administering to a subject in need of such treatment (i) a therapeutically effective amount of a compound according to any one of claims 1 to 18, or a pharmaceutically acceptable salt thereof, or (ii) a pharmaceutical composition according to claim 19. 24. Use of a compound according to any one of claims- 1 to 18, or a pharmaceutically acceptable salt thereof, for treating a bacterial infection, or in the manufacture of a medicament for treating a bacterial infection. 25. The method of claim 20 or the use of claim 21, wherein the bacterial infection is due to Pseudomonas spp., Klebsiella spp., Enterobacter spp., Escherichia spp., Morganella spp., Citrobacter spp., Serratia spp. or Acintetobacter spp.