1. Polyamide 56 filaments characterized by having a relative viscosity in sulfuric acid of 3 to 8, an Mw/Mn ratio of 1.5 to 3, a single fiber fineness of 0.1 to 7 dtex, a strength of 7 to 12 cN/dtex, a shrinkage rate of 5 to 20% after having been subjected to boiling water treatment at 98°C for 30 minutes, a strength of 5 to 11 cN/dtex after the boiling water treatment and a stress at 10% elongation of 0.3 to 1.5 cN/dtex after the boiling water treatment.
2. Polyamide 56 filaments, as claimed in claim 1, which have an overall fineness of 200 to 600 dtex.
3. A process for producing polyamide 56 filaments comprising the steps of forming spun fibers using a polyamide 56 resin having a relative viscosity in sulfuric acid of 3 to 8 and an Mw/Mn ratio of 1.5 to 3, wherein the polyamide 56 resin is produced by a process comprising the steps of subjecting the raw materials with the ratio of the number of moles of 1,5-pentamethylenediamine to the number of moles of adipic acid kept in a range from 0.95 to 1.05, to pressure-heat polymerization in the presence of water, to produce pellets of a resin having the following properties (1) to (3), subsequently stirring said pellets with the temperature in the reactor kept in a range from 130 to 200°C while reducing the pressure to 133 Pa or lower, and performing solid phase polymerization for 1 to 48 hours;

(1) Relative viscosity in sulfuric acid: 2.9 or lower
(2) 0.3 < [NH2]/([NH2] + [COOH]) < 0.7
[NH2]: Amino end group concentration in the polyamide 56 resin subjected to solid phase polymerization (eq/ton)
[COOH]: Carboxyl end group concentration in the polyamide 56 resin subjected to solid phase polymerization (eq/ton)
(3) Size of pellets: 2 to 70 mg/pellet,
solidifying the spun fibers by cooling air, subsequently applying a water-

free oil, taking up at 300 to 2000 m/min, subsequently stretching at such an stretching ratio as to ensure that the obtained filaments can have an elongation rate of 10 to 50%, heat-treating with the temperature of the final heat treatment roll kept at 210 to 250°C, subsequently relaxing at a relaxation ratio of 0.8 to 0.95, and subsequently winding.