A process for the production of a polyurethane hot-melt adhesive based on grafted polyester-polyether block copolymers with grafted-on hydroxyl groups and the reaction thereof with a stoichiometric excess of a polyisocyanate and the optional mixing thereof with further pre-polymers based on polyether polyols and polyester polyols is disclosed. By this process, the polyester-polyether block copolymers are firmly incorporated into the polyurethane matrix on curing, so that they are migration-proof. Highly-elastic hot-melt adhesives result, which, with optional foaming, are also suitable for the production of elastic seals.