A damper device including first and second support members, one of which is fixed to a support element and the other of which is fixed to a suspended element, an elastic block made of a deformable, elastic material for elastically coupling the two support members and a sealed space formed therein filled with a liquid. One partition member has its periphery fixed to the first support member and divides the sealed space into two chambers. The partition member has therein a member movable along a short distance. Fluid passages are formed in a wall portion of the first support member so as to communicate between the two chambers and to impart flow resistance to the liquid flowing therethrough. The partition member can be suspended to the first support member by an elastic sheet and be movable along the axial direction of the first support member. A solenoid is mounted on the inner wall of the first support member. When the solenoid is energized, the partition member can be fixed to the first support member. When the damper device is used in an engine suspension of a vehicle with vibrations of high frequency and small magnitude of vibration, relative movement of the first and second support members is damped by displacement of the movable member of the partition member. With low-frequency vibrations, vibrations having a relatively large magnitude are damped by the flow resistance of the liquid flowing through the fluid passages. When the engine is in the idling mode, the solenoid is deenergized, and the partition member is kept movable.