In a process for spin-dyeing an acid-modified polymer or copolymer of acrylonitrile with a quaternary dyestuff according to the wet-spinning procedure, the improvement consisting essentially of employing, as a quaternary dyestuff, a dyestuff which has a migration factor M of 20 or less, a combination index K of less than 2.5 and a cation weight CW of more than 310, and which corresponds to the formula ##STR116## in which D.sup.(+), being identical to or different from one another, each is the radical of a quaternary ammonium, lower dialkylhydrazonium or cycloammonium diazo component,
- Q.sub.3 is lower alkylene or lower alkylene interrupted by --O--, --NH-- or an aromatic carbocyclic radical,
- R.sub.1 and R.sup.2, being identical to or different from one another, each is hydrogen or lower alkyl or lower alkyl substituted by one or two of the substituents hydroxy, acetoxy, lower alkoxy, cyano, lower carbalkoxy, chlorine, phenyl;
- phenyl substituted by halogen, lower alkyl, lower alkoxy, nitro, acetylamino, sulfamoyl or carbamoyl;
- carbamoyl and carbamoyl substituted by lower alkyl, a phenyl, or a benzyl;
- or
- R.sub.1 and R.sub.2 conjointly with the two nitrogen atoms and the radical Q.sub.3 form a heterocyclic ring,
- the benzene nuclei a and b each are unsubstituted or substituted in an identical or different manner, the substituents being 1 or 2 of the substituents lower alkyl, lower alkoxy, halogen trifluoromethyl or lower alkanoylamino, or
- the benzene nuclei a or b or both contain a fused benzene ring thus forming in a naphthylene, and
- X.sup.(-) is the equivalent of an anion.