The invention concerns a process for making a scrim-reinforced prepreg for use in building low-porosity lay-ups, characterized in that a conventional prepreg is formed of a fibrous reinforcement and a heat-curable resin, the prepreg having suitable viscosity and sufficient tackiness to hold a scrim which is adhered to the prepreg by applying light pressure, so that the scrim is impressed onto the prepreg to such a degree, that less than half of the circumference of the scrim strands becomes coated by the prepreg-resin.