A process for the continuous dyeing of fiber material of one or more acid-modified polymers or copolymers of acrylonitrile in the gel state, said fiber material having been produced by wet spinning from a spinning solution containing one or more organic solvents, which process comprises dyeing the fiber material with a solution of a carbinol base or anhydro base of a carboxyl- or sulfo-free N-arylated triarylmethane dyestuff, a carboxyl- or sulfo-free N-arylated diarylindolylmethane dyestuff, a carboxyl- or sulfo-free N-arylated oxazine dyestuff, a carboxyl- or sulfo-free N-arylated xanthene dyestuff, or a carboxyl- or sulfo-free N-arylated azine dyestuff in a dye bath containing water and the organic spinning solvent or solvents.