The invention relates to a hybrid component part comprising a local stiffening made of a two-stage-crosslinked polyurethane-based fiber composite material, more particularly to the production of such a hybrid component part. Said invention has for its object to specify a technology which makes it possible in cost-effective fashion to effect local stiffening of metal parts with a fiber composite material in order thus to obtain a hybrid component part. It is a fundamental concept of the process according to the present invention to use a particular polyurethane formulation which in a first crosslinking reaction can be converted into a thermoplastic polymer and later in a second crosslinking reaction is fully crosslinked to afford a thermoset matrix material. The thermoplastic polymer is characterized by a good adhesion to metal surfaces. The metal can be subjected to further forming with the attached thermoplastic material. The polyurethane is subsequently thermosettingly cured and achieves its final stiffness.