A method for the preparation of prepregs comprisesI. impregnating a fibrous reinforcing material with a liquid composition containing an epoxide resin, a photopolymerizable compound, and with a heat-activated curing agent for epoxide resins, andIi. in the absence of a substance which gives rise to a substantial degree of photoinduced polymerization through consumption of epoxide groups, exposing the impregnated material to actinic radiation such that the composition solidifies due to photopolymerization of the said photopolymerizable compound while the epoxide resin remains substantially in the thermosettable state.Preferably the liquid composition also contains a dual-functional substance which has in the same molecule both an epoxide group and a dissimilar group through which the substance can be photopolymerized. The prepreg, optionally after shaping and/or stacking, is heated to cure the epoxide resin and, if used, the photopolymerized dual-functional substance.