A device for abating vibrations in a cutter bar (12) with alternating motion coupled with a supporting and transmission group (20) connected to a power takeoff (46) of the mower (11), said supporting and transmission group (20) comprising a kinematic transformation system of a rotary motion coming from said power takeoff (46) into a motion of the movable blade (17) which is flat with an alternating movement, in a transversal direction with respect to the advance direction of the mower and perpendicular to an axis of the power takeoff (46), wherein said movable blade is kept in engagement on cutting elements (15) constrained to the supporting and transmission group (20), the device providing that a further second kinematic system is associated with the first kinematic transformation system of the rotary motion into a flat motion with an alternating movement of the movable blade (17), for the alternating backwards and forwards movement of a balancing mass (37) in an opposite direction to that of the movable blade (17), wherein the second further kinematic system is moved by the first kinematic system.
