A process for producing moldings comprising oxazolidinone groups, wherein a) polyisocyanate is mixed with b) at least one organic compound having two or more epoxide groups, c) at least one catalyst for the isocyanate/epoxide reaction, and d) optionally auxiliary and additive materials to form a reaction mixture, and reacted to form moldings comprising oxazolidinone groups, where the catalyst c) for the isocyanate/epoxide reaction comprises a compound of the general formula [M(R 1 )(R 2 )(R 3 )(R 4 )] + [X I n ] - , where M is a nitrogen atom or a phosphorus atom, R 1 , R 2 , R 3 and R 4 are an organic radical, in each case selected independently of one another from the group consisting of linear or branched-chain alkyl radicals having 1 to 22 carbon atoms and being possibly substituted by heteroatoms or substituents comprising heteroatoms, and of alkyl-bridged cycloaliphatic or aromatic groups having 3 to 22 carbon atoms and being possibly substituted by heteroatoms or groups comprising heteroatoms, and of aryl radicals having 6 to 18 carbon atoms and being possibly substituted by alkyl groups having 1 to 10 carbon atoms and/or heteroatoms, X is fluoride, chloride, bromide or iodide, I is iodine, and n stands for rational numbers from 0.1 to 10. a) polyisocyanate is mixed with b) at least one organic compound having two or more epoxide groups, c) at least one catalyst for the isocyanate/epoxide reaction, and d) optionally auxiliary and additive materials to form a reaction mixture, and reacted to form moldings comprising oxazolidinone groups, where the catalyst c) for the isocyanate/epoxide reaction comprises a compound of the general formula [M(R 1 )(R 2 )(R 3 )(R 4 )] + [X I n ] - , where M is a nitrogen atom or a phosphorus atom, R 1 , R 2 , R 3 and R 4 are an organic radical, in each case selected independently of one another from the group consisting of linear or branched-chain alkyl radicals having 1 to 22 carbon atoms and being possibly substituted by heteroatoms or substituents comprising heteroatoms, and of alkyl-bridged cycloaliphatic or aromatic groups having 3 to 22 carbon atoms and being possibly substituted by heteroatoms or groups comprising heteroatoms, and of aryl radicals having 6 to 18 carbon atoms and being possibly substituted by alkyl groups having 1 to 10 carbon atoms and/or heteroatoms, X is fluoride, chloride, bromide or iodide, I is iodine, and n stands for rational numbers from 0.1 to 10. M is a nitrogen atom or a phosphorus atom, R 1 , R 2 , R 3 and R 4 are an organic radical, in each case selected independently of one another from the group consisting of linear or branched-chain alkyl radicals having 1 to 22 carbon atoms and being possibly substituted by heteroatoms or substituents comprising heteroatoms, and of alkyl-bridged cycloaliphatic or aromatic groups having 3 to 22 carbon atoms and being possibly substituted by heteroatoms or groups comprising heteroatoms, and of aryl radicals having 6 to 18 carbon atoms and being possibly substituted by alkyl groups having 1 to 10 carbon atoms and/or heteroatoms, X is fluoride, chloride, bromide or iodide, I is iodine, and n stands for rational numbers from 0.1 to 10. <EOS>