A machine for making absorbent sanitary articles includes a device for feeding a continuous strip to a conveyor roller and to a device for cutting the strip into first and second pieces. A unit forms and applies at least a pair of first and second pieces, aligned and spaced by a distance (d), for each absorbent article A first and a second roller each comprising a plurality of units pick up and successively release of first and the second pieces. A plurality of concentric units rotating, independently of each other, about a shared axis of rotation, each carries at least one unit. A motor defines a respective law of motion for each of the units and a mechanism translates the units, between a position for picking up the pieces, at the conveyor roller, and a position for releasing the pieces, at the forming and applying unit.