Abstract: The present invention relates to a hydroxy-functional copolymer P, which is present as a dispersion and/or solution in water, and is obtained by successively carrying out process steps A-D: A) initially introducing a hydrophobic polymer containing hydroxyl groups into a reaction vessel, B) introducing an initiator component into that vessel, C) subsequently polymerizing a hydrophobic monomer mixture containing hydroxyl groups in that vessel and D) subsequently polymerizing a hydrophilic monomer mixture containing hydroxyl and acid groups in that vessel. The present invention also relates to a process for the preparation of copolymers P following the procedure previously set forth and to coating compositions containing these copolymers P and one or more crosslinking agents.