Abstract: The present invention relates to thermoplastically formable composite materials of reinforcing fibers in a polyamide 12 matrix, characterized in that the polyamide 12 matrix consists of anionically polymerized laurin-lactam maximally containing 15 weight-% of co-monomers and selectively additives which are determined on the basis of production, processing and use. The invention furthermore relates to a process for producing these composite materials, in accordance with which an activated anionic lactam 12 melt is prepared, which penetrates the fiber arrangement in the liquid state, so that it forms the matrix for a shaped body, the activated melt is final-polymerized under the effects of temperature and pressure in a mold or a tool in such a way that the shape is achieved, and the pre-formed part is subjected to an after-shaping step under the effects of pressure and temperature, if desired.