Hydraulic vibration damping device intended to be inserted for the purposes of damping between first and second rigid elements, with this vibration damping device comprising: - first and second frames (2, 3) intended to be fixed to the two rigid elements to be joined, - an elastomer body that connects first and second frames together and which delimits at least partially a first hydraulic chamber, - a second hydraulic chamber which is delimited by a deformable wall and which communicates with the first hydraulic chamber by the intermediary of a constricted passage, with the first and second hydraulic chambers and with the constricted passage forming a hydraulic circuit filled with liquid, - an electromagnetic actuator suited to control the vibration damping behaviour of the vibration damping device, characterised in that said actuator comprises a suction cup with a permanent magnet comprising: - a magnetic circuit (28, 34, 40) including an actuating member mobile entre a first position and a second position, - at least one spring soliciting the actuating member with a first force directed towards the first position, - a permanent magnet creating a permanent magnetic field in the magnetic circuit and soliciting the actuating member with a second force directed towards the second position, with the first force being greater than the second force when the actuating member is in the first position and with the second force being greater than the first force when the actuating member is in the second position, - at least one coil electrically supplied by a control device, with the control device being suited to selectively either increase said magnetic field in order to have said actuating member pass from the first to the second position against the solicitation of the spring, or to decrease said magnetic field in order to have said actuating member pass from the second to the first position under the effect of the spring. - first and second frames (2, 3) intended to be fixed to the two rigid elements to be joined, - an elastomer body that connects first and second frames together and which delimits at least partially a first hydraulic chamber, - a second hydraulic chamber which is delimited by a deformable wall and which communicates with the first hydraulic chamber by the intermediary of a constricted passage, with the first and second hydraulic chambers and with the constricted passage forming a hydraulic circuit filled with liquid, - an electromagnetic actuator suited to control the vibration damping behaviour of the vibration damping device, - a magnetic circuit (28, 34, 40) including an actuating member mobile entre a first position and a second position, - at least one spring soliciting the actuating member with a first force directed towards the first position, - a permanent magnet creating a permanent magnetic field in the magnetic circuit and soliciting the actuating member with a second force directed towards the second position, with the first force being greater than the second force when the actuating member is in the first position and with the second force being greater than the first force when the actuating member is in the second position, - at least one coil electrically supplied by a control device, with the control device being suited to selectively either increase said magnetic field in order to have said actuating member pass from the first to the second position against the solicitation of the spring, or to decrease said magnetic field in order to have said actuating member pass from the second to the first position under the effect of the spring.