The invention relates to a process for the stabilization of a spinning solution of an acrylonitrile polymer and a solvent which comprises adding from 0.005 to 0.5% based on the quantity of polymer of at least one stabilizer selected from a polyfunctional phosphonic acid, a phosphonocarboxylic acid or a polymer containing phosphonic acid and/or carboxyl groups to the spinning solution as well as to such stabilized spinning solutions.