Described is an NCO-group-containing polyurethane prepolymer madefrom polyisocanyates and polyols derived from natural oils. The invention is characterized in that the polyol is obtained by transesterification in the presence of basic lithium compounds. Together with a tertiary amine used to accelerate the moisture curing, the storage stability is thus increased considerably. Up to 4.0 mmol of the lithium compound is used per kilogram of polyol, and 0.1 to 2.0% by wt. of the amine, relative to the total weight of the composition, is used as the accelerator. The polyurethane prepolymer is suitable not only for the production of adhesives but also for the production of foamed materials, in particular those dispensed from throw-away pressure vessels.