Impact-resistant polyoxymethylene molding materials containing(A) from 30 to 95% by weight of one or more polyoxymethylenes and(B) from 5 to 70% by weight of one or more elastomeric graft polymers which are prepared by emulsion polymerization, are dispersed in component A, have a mean particle diameter of from 0.08 to 2 .mu.m and are composed of1. from 60 to 90% by weight of a grafting base of crosslinked polybutadiene in which not more than 30% by weight of the butadiene may be replaced with isoprene, 2,3-dimethylbutadiene, styrene, p-methylstyrene, .alpha.-methylstyrene and/or (meth)acrylonitrile, and2. from 10 to 40% by weight of one or more grafted shells consisting of polymers of styrene and/or methyl methacrylate, in which not more than 15% by weight of the said monomers 2 may be replaced with acrylonitrile or a C.sub.1 -C.sub.8 -alkyl acrylate,the percentages A and B and the percentages 1 and 2 summing to 100, with or without(C) effective amounts of assistants,and a process for their preparation.