A process for building tyres provides for building a carcass sleeve around a forming drum having an application diameter and two lateral half-portions axially moveable relative to each other. The carcass sleeve comprises at least one carcass ply coaxially engaged around each of the axially opposite end flaps thereof to an annular anchoring structure defining a fitting diameter smaller than the application diameter. The building of the carcass sleeve comprises: applying and stopping a leading end of a semi-finished product in form of continuous strip cut to size against a continuous surface of the forming drum; winding the semi-finished product in form of continuous strip cut to size circumferentially around the forming drum; joining a trailing end of the semi-finished product to the leading end at said continuous surface. The continuous surface is extended only partly around the forming drum. The semi-finished product, except for the leading end and the trailing end, is laid against a discontinuous circumferential surface of the forming drum adjacent to the continuous surface and belonging to the two lateral half-portions.