An oscillating-piston engine comprises a housing, in which several pistons configured as two-armed levers are arranged pivotably, respectively, around a pivot axis being parallel to a central housing axis and movable commonly in a revolution direction. The pistons comprise running surfaces on their side facing away from the housing inner wall, which are guided alongside at least one control cam when the pistons revolve in the housing, of a centrally housing-fixed cam piece, in order to control the pivot movements of the pistons in revolution. The control cam is configured as inner contour on the cam piece, alongside of which the pistons are guided supported to the side of the centrifugal force via the running surfaces. The cam piece comprises another, inner contour configured as a control cam alongside of which the pistons are guided supported to the direction of the central housing axis via the running surfaces.