Process for the production of moldings from nanoporous polymer materials, comprising the stages of a) preparation of a multiphase polymer mixture with domains in the range from 5 to 200 nm, b) impregnation of the polymer mixture with a blowing agent, where the solubility of the blowing agent in the phase forming the domains is at least twice as high as in the adjacent phases, c) expansion of the multiphase polymer mixture comprising blowing agent, by introducing the polymer mixture into a cavity and expanding it therein, thus obtaining the molding.