The present invention relates to a process for preparing a polyurethane, comprising the reaction of a composition (Z1) at least comprising a compound (P1) reactive toward isocyanates, and a composition (Z2) at least comprising a polyisocyanate, wherein compound (P1) is obtained by the reaction of at least one polyepoxide with a compound (V1) selected from the group consisting of polyetheramines and polyetherols. The present invention further relates to polyurethanes obtained by such a process, and to the use of a polyurethane of the invention for coating of pipelines, as a “field joint” or of subsea equipment, for example “christmas trees”, for the offshore sector, and as a glass-syntactic polyurethane.