A controllable hydraulic vibration-damping support comprising two strength members interconnected by an elastomer body defining a working hydraulic chamber, an auxiliary hydraulic chamber communicating with the working chamber via a constricted passageway, a pneumatic chamber separated from the auxiliary chamber by a moving wall, an electrically controlled vent device for establishing a connection to the air, which device can be actuated electrically in order to put the pneumatic chamber into communication with the atmosphere, and a check valve allowing air to flow only out from the pneumatic chamber towards the atmosphere.