A dual seal assembly, in particular for sealing a gas compressor, includes a first mechanical seal assembly including a pair of co-operating seal rings, one of which is provided for common rotation with a rotating component and the other of which is provided rotationally fixed at a stationary component. A second mechanical seal assembly includes a pair of co-operating seal rings, one of which is provided for common rotation with a rotating component and the other of which is provided rotationally fixed at a stationary component. One of the seal rings is axially movable and axially biased with a biasing force against the respectively other seal ring to bias facing sliding surfaces of the seal ringss in a mutual sealing engagement. A secondary sealing assembly is provided for sealing the axially movable seal ring with respect to at least one circumferential guiding surface of a guiding component.