An apparatus for building pneumatic tyres includes a forming support and an assembling device to assemble components of elastomeric material on the forming support. The assembling device includes a feeding unit to deliver a continuous elongated element of elastomeric material, a conveyor having a moving surface along a predetermined direction and toward a proximal end thereof close to the forming support, and an application device positioned at the proximal end. The continuous elongated element is moved forward on the moving surface as far as the proximal end and the forming support is rotated to enable application of the continuous elongated element in the form of coils wound up on the forming support itself. A retaining device co-operates with the conveyor to brake the continuous elongated element at the end of the application, while the forming support goes on rotating, until it causes stretching and severing of the continuous elongated element.