A process for the preparation of expandable thermoplastic polymers by post-impregnation with a blowing agent in aqueous suspension in the presence of a mixture of magnesium pyrophosphate and a sulfonate group-containing extender as suspension stabilizer, in a reactor comprisesa) preparing the magnesium pyrophosphate in the same reactor at below 50.degree. C. by adding a solid magnesium salt in an amount corresponding to an at least 3% stoichiometric excess, based on pyrophosphate, to an aqueous solution of the pyrophosphate,b) heating the suspension medium to from 70.degree. to 140.degree. C. andc) adding the blowing agent in this temperature range.