Process for producing very fine denier synthetic fibers

A process for the production of synthetic acrylonitrile fibers and filaments having at least 40% by weight acrylonitrile units and individual as spun deniers of 3 dtex and less from filament-forming synthetic polyacrylonitrile polymers containing at least 40% by weight acrylonitrile units by a dry spinning process and further treating the spun material in a manner known per se to produce finished fibers or filaments, comprising spinning a viscosity-stable spinning solution in an organic solvent under thermal conditions such that a draft of at least 30 is established.