The invention relates to a process for producing a prepreg based on polyurethane, which is notable for high storage stability at room temperature, a two-stage reaction mechanism, and adjustable adhesion on metal surfaces. It is based on the problem of making the surface tack of the prepregs controllable during processing. The solution is to assemble the PU mixture from which the matrix originates at a later stage such that the glass transition temperature of the thermoplastic polymer is above 30° C. For this purpose, the invention proposes two basically independent but certainly synergistic measures, namely: i) use of a polyol compound or a mixture of a number of polyol compounds as binder, the OH number or mean OH number of which is above 300 mg KOH/g, ii) choice of the proportion of hardener corresponding to the co-binder in the reactive composition at greater than 2% by weight, based on the total solids content of the reactive composition.