An anti-roll device equips an axle assembly of a motor vehicle and comprises two connecting rods of which one comprises a part of coupling means comprising: a housing subdivided into two parts by a piston and comprising two inlets-outlets communicating with the two parts and an intermediate inlet-outlet communicating with at least one of the parts depending on the position of the piston, a fluid reservoir supplying a conduit coupled to the intermediate inlet-outlet, two non-return means coupled to the inlets-outlets and to the conduit, and an electrically operated valve coupled to the inlets-outlets and placed either in an open state ensuring a connection between the parts and the fluid reservoir via the intermediate inlet-outlet, or in a closed state allowing fluid discharge out of the housing only through the intermediate inlet-outlet.