Abstract: Impact-resistant modified styrene polymers having the characteristics: molecular weight M.sub.v 150,000 to 170,000; gel content exceeding 22%; degree of swelling of 11.5 to 13.5 and a mean gel particle diameter of 1.7 to 4.5 microns are produced by continuously polymerizing a styrene solution of polybutadiene, possibly in the presence of diluents, by means of a cascade consisting of at least three continuous stirred tank reactors, at rising temperatures and in the presence of organic peroxide initiators. The process steps are carried out as follows:(a) in a first continuous stirred tank reactor, a continuously introduced solution of styrene containing from 8 to 10.