A mechanical seal assembly, comprising a mechanical seal (2a, 2b) comprising a rotating slide ring and a stationary slide ring, defining a sealing gap at sliding surfaces which are opposite to each other, and a fluid circuit comprising a pump assembly for supplying a fluid to the mechanical seal (2a, 2b), comprising: - exactly one drive comprising a drive shaft, - a first axial pump, which conveys the fluid in the axial direction (X-X) of the drive shaft, - a second axial pump, which conveys the fluid in the axial direction of the drive shaft and - a radial pump, which conveys the fluid in the radial direction of the drive shaft, - wherein the first axial pump and the second axial pump, in flow-through direction of the fluid across the pump assembly, are arranged in front of the radial pump, and - wherein the drive simultaneously drives the first axial pump, the second axial pump and the radial pump, and - further comprising a magnetic coupling comprising an input part having first permanent magnets, a fixed hollow cylinder and an output part having second permanent magnets, - wherein the first permanent magnets, in the axial direction (X-X) of the drive shaft, are offset by a distance in relation to the second permanent magnets, wherein the first permanent magnets partially overlap the second permanent magnets in the radial direction, - wherein the first axial pump conveys the fluid in a first axial direction and the second axial pump conveys the fluid in a second axial direction, which is opposite to the first axial direction, - wherein the first axial pump and the second axial pump are formed as conveying thread pumps, and - wherein the output part comprises a first radial bearing and a second radial bearing and - wherein the pump assembly comprising exactly one axial bearing for axially supporting the output part. - exactly one drive comprising a drive shaft, - a first axial pump, which conveys the fluid in the axial direction (X-X) of the drive shaft, - a second axial pump, which conveys the fluid in the axial direction of the drive shaft and - a radial pump, which conveys the fluid in the radial direction of the drive shaft, - wherein the first axial pump and the second axial pump, in flow-through direction of the fluid across the pump assembly, are arranged in front of the radial pump, and - wherein the drive simultaneously drives the first axial pump, the second axial pump and the radial pump, and - further comprising a magnetic coupling comprising an input part having first permanent magnets, a fixed hollow cylinder and an output part having second permanent magnets, - wherein the first permanent magnets, in the axial direction (X-X) of the drive shaft, are offset by a distance in relation to the second permanent magnets, wherein the first permanent magnets partially overlap the second permanent magnets in the radial direction, - wherein the first axial pump conveys the fluid in a first axial direction and the second axial pump conveys the fluid in a second axial direction, which is opposite to the first axial direction, - wherein the first axial pump and the second axial pump are formed as conveying thread pumps, and - wherein the output part comprises a first radial bearing and a second radial bearing and - wherein the pump assembly comprising exactly one axial bearing for axially supporting the output part.