A piston-cylinder assembly for a centrifugal piston compressor, comprising a piston; a cylinder bore in which the piston is arranged displaceably along a center line of the cylinder bore; a drive shaft with an axis of rotation and with a cylindrical eccentric, the center of which is spaced from the axis of rotation of the drive shaft, wherein the piston can be moved by the cylindrical eccentric during a rotary movement of the drive shaft in the cylinder bore in a radial direction away from the drive shaft in an outward direction up to a top dead center; and a transmission element which transmits the movement of the eccentric to the piston in order to generate the outward movement of the piston in the cylinder bore directed away from the drive shaft, the transmission element having a first supporting surface with which the transmission element is supported on a cylindrical surface of the eccentric; wherein the piston has a concave-shaped first active surface facing the transmission element and the transmission element has a convex-shaped second supporting surface facing the first active surface, wherein the first active surface and the second supporting surface form a positive connection effective in the circumferential direction of the eccentric, and wherein a cylindrical piston guide ring is provided, by means of which the piston can be moved in the cylinder bore starting from the top dead centre in a radial direction inwards towards the drive shaft up to a bottom dead centre, characterized in in that the piston has a convexly shaped second active surface which faces an inner surface of the piston guide ring and forms a positive connection with the inner surface of the piston guide ring which is effective in the direction of the center line of the cylinder bore. a cylinder bore in which the piston is arranged displaceably along a center line of the cylinder bore; a drive shaft with an axis of rotation and with a cylindrical eccentric, the center of which is spaced from the axis of rotation of the drive shaft, wherein the piston can be moved by the cylindrical eccentric during a rotary movement of the drive shaft in the cylinder bore in a radial direction away from the drive shaft in an outward direction up to a top dead center; and a transmission element which transmits the movement of the eccentric to the piston in order to generate the outward movement of the piston in the cylinder bore directed away from the drive shaft, the transmission element having a first supporting surface with which the transmission element is supported on a cylindrical surface of the eccentric; wherein the piston has a concave-shaped first active surface facing the transmission element and the transmission element has a convex-shaped second supporting surface facing the first active surface, wherein the first active surface and the second supporting surface form a positive connection effective in the circumferential direction of the eccentric, and wherein a cylindrical piston guide ring is provided, by means of which the piston can be moved in the cylinder bore starting from the top dead centre in a radial direction inwards towards the drive shaft up to a bottom dead centre, characterized in in that the piston has a convexly shaped second active surface which faces an inner surface of the piston guide ring and forms a positive connection with the inner surface of the piston guide ring which is effective in the direction of the center line of the cylinder bore.