On a wrapping machine, the products for wrapping are transferred along a portion of a wrapping line by a transfer wheel, which has a number of radially projecting gripper-type peripheral seats, and rotates in steps about an axis of rotation to feed the peripheral seats in a given direction through a loading station, where each peripheral seat receives a relative product by means of a first transfer assembly, and through an unloading station where each product is expelled from the relative peripheral seat and fed through a wrapping assembly by means of a second transfer assembly; each peripheral seat having a first and a second jaw, of which the second jaw, located behind the first, is movable between a closed position and an open position.