A slide ring seal assembly includes a slide ring member and a counterring member adjoining the slide ring member in axial alignment therewith. A force-exerting arrangement which axially resiliently presses the two ring members to one another includes a first resilient sealing ring being coaxial with and engaging one of the ring members; and a second resilient sealing ring being coaxial with and engaging the other of the ring members. The first and second sealing rings are in a radial alignment with one another and are stressed by clamping arrangements, so that the sealing rings exert axial forces on the two ring members, pressing them together. At least the first sealing ring and the first clamping arrangement are so designed that the axial restoring force generated by virtue of the deformation of the first sealing ring seeks to reduce the axial dimension of the resiliently deformed first sealing ring. Such an axial restoring force constitutes the axial pressing force exerted by the first sealing ring.