Process for the production of polymers containing acrylonitrile

Acrylonitrile polymers and copolymers with good affinity for basic dyes without sulfonic acid groups containing comonomers are obtained by polymerizing at a temperature of from 0 DEG to 60 DEG C. in an aliphatic hydrocarbon having a boiling point of from -10 DEG to 80 DEG C. or in a mixture of aliphatic hydrocarbons having boiling points in the range from -10 DEG to 80 DEG C. using an initiator system comprising from 0.1 to 8.0 mole percent of sulfur dioxide, from 0.1 to 2.0 mole percent of a hydroperoxide which is soluble in the reaction medium and from 0.01 to 1.0 mole percent of an acid which is soluble in the reaction system in that polymerization is carried out continuously and in that an average residence time of from 10 minutes to 2 hours is maintained.