A lubrication system for a rotary-piston internal combustion engine of the trochoid type with a multi-arc-shaped trochoidal surface and a multi-cornered piston supported on a roller bearing. A dosed quantity of lubricating oil is supplied through an axial bore in the shaft and radial bores in the eccentric into the axial center of the bearing of the eccentric. The outer bushing of this bearing has a U-shaped axial cross-sectional shape and is provided with central radial bores which are aligned with bores in the piston and communicate with axial channels in the piston, the latter channels leading to radial bores in the internal gear of the mechanism. The cross-sectional aperture of these bores may be used to control the quantity of oil supplied to the gear mechanism.