A process for the production of crimped filaments and fibers of acrylonitrile polymers of copolymers containing at least 40% by weight acrylonitrile units, by dry spinning from highly polar solvents, where the filaments are brought to extremely low solvent contents in the actual spinning tube by a minimum of superheated steam prepared in the absence of water at very high spinning tube temperatures and spinning gas temperatures, but are cooled to low filament temperatures in the spinning tube by application of water or aqueous finishes in a quantity equivalent to more than 10% by weight moisture. In this way, spun PAN filaments of good natural color are safely obtained, in which there is no washing stage and no drying stage. Acrylic fibers and filaments combining a vacuolestable structure with a very high degree of whiteness and gloss are thus obtained with densities of at least 1.180 g/cm.sup.3, giving shrinkage-free to high-shrinkage fibers, depending on the aftertreatment applied.