An oscillating piston engine is described, having a housing (12) which has an at least approximately spherical inner wall (32), and having at least two pistons (34, 36) which can jointly revolve in the housing (12) about a fixed rotation axis (42) and, when revolving about the rotation axis (42), perform back-and-forth swivelling movements about at least one swivel axis (44) perpendicular to the rotation axis (42), wherein the swivelling movements of the two pistons (34, 36) are in opposition to one another, and wherein the two pistons (34, 36) each have an end face (46, 48), said end faces (46, 48) facing one another and each defining a front end of a working chamber (54) which is arranged completely outside the rotation axis (42) and is defined at the circumference by a working chamber wall (58). The working chamber (54), formed by the two end faces (46, 48) of the two pistons (34, 36) and the working chamber wall (58), and the pistons (34, 36) have the shape of a toroid section at least in the region of their ends facing the working chamber (54).