A fluid-filled vibration damper includes a partition which is vibratable to absorb vibrations with small amplitudes. When vibrations with amplitudes greater than a certain amplitude level are continuously applied over a certain period of time, the vibrations of the partition are substantially stopped. The fluid-filled vibration damper comprises an attachment adapted to be attached to a vibration source, a base adapted to be attached to a structural member, an elastomeric member interconnecting the attachment and the base, a diaphragm disposed in either the attachment or the base, the elastomeric member and the diaphragm defining therebetween a fluid chamber filled with a fluid, a partition disposed in the fluid chamber and dividing the fluid chamber into first and second fluid chambers, a passage providing fluid communication between the first and second fluid chambers, and a stop assembly disposed between the partition and the first fluid chamber and between the partition and the second fluid chamber and spaced from the partition with a clearance therebetween, the stop assembly limiting vibration of the partition while allowing the partition to move transversely within a predetermined range, the partition having therein an auxiliary fluid chamber having a variable volume and communicating with at least one of the first and second fluid chambers, the auxiliary fluid chamber being expandable to reduce the clearance between the partition and the stop assembly when the fluid flows from said at least one fluid chamber into the auxiliary fluid chamber.