In a process of manufacturing pneumatic tires, a carcass sleeve is made which includes at least one carcass ply provided with axially opposite flaps turned up around annular anchoring structures, so as to form respective loops. An outer sleeve is positioned around the carcass sleeve and the latter is radially expanded in order to cause application of same against a radially internal surface of the outer sleeve. After each of the end flaps has been turned up and before radial expansion, only a portion belonging to each of the loops and extending substantially parallel to the respective annular anchoring structure is submitted to a step of carrying out heating under pressure, to make each loop integral with the annular anchoring structure and prevent the turned-up ply/plies from even partly slipping off, during the subsequent radial-expansion step of the carcass sleeve and vulcanization step of the tire.