The device comprises at least a continuous movable flexible member (23) carrying a series of contact members (29, 29A, 29B) for the products (R; R1; RN) aligned with one another. A section of the movable flexible member is devoid of said contact members to allow the trimmings (Rc, Rt) to fall. At least a longitudinal supporting element (21) of the products (R; R1, RN), is also provided, parallel to the movable flexible member, the reciprocal position of said flexible member and of said longitudinal element being such that the products advance in contact with the contact members (29, 29A, 29B) of the flexible member and with the longitudinal element. A pusher (11) inserts the series of products with the respective trimmings between the flexible member and the longitudinal supporting member. The flexible member (23) is controlled with a variable speed to carry the section thereof devoid of contact members time by time to the level of the head and tail trimmings (Rc; Rt) of two consecutive series of products.