A process is described for the preparation of high-molecular weight white polyamides, substantially consisting of units of --NH--(CH.sub.2).sub.4 --NH--CO(CH.sub.2).sub.4 --CO--, by the after-condensation of a corresponding low-molecular prepolymer, consisting substantially of a molecular chain of units of --NH--(CH.sub.2).sub.4 --NH--CO(CH.sub.2).sub.4 --CO--, in which process the prepolymer which is employed has been prepared in the presence of an excess of 0.5 to 15 moles-% of 1,4-diaminobutane with respect to the quantity stoichiometrically equivalent to the adipic acid applied. This prepolymer is thereafter subjected to the after-condensation reaction in the solid phase in an atmosphere containing water vapor.