A piston machine comprises a housing, in which at least one first piston is arranged which can be moved to and fro between two end positions in order to periodically increase and reduce the size of a working chamber adjoining a first end face of the at least one first piston, the at least one first piston having at least one guiding member, which is in engagement with a control curve which is formed on a curve member arranged in the housing, the curve member extending concentrically and circumferentially in the housing, all the way round an axis of revolution which is fixed relative to the housing, and being arranged radially to the outside of the piston in relation to the axis of revolution, a second piston being situated opposite the at least one first piston and performing opposing reciprocating movements relative to the first piston, the second piston having a second end face, which faces the first end face of the first piston, and the working chamber being situated between the end faces. The curve member is mounted in the housing in such a way that it can revolve about the axis of revolution, while the at least one first piston and the second piston cannot revolve about the axis of revolution, with the result that the at least one first piston and the second piston perform reciprocating movements in a plane of movement which is fixed relative to the axis of revolution when the curve member revolves about the axis of revolution.