An internal combustion engine having combustion chambers that rotate about a main shaft axis in a step-wise manner. A first and second rotors each have elongate pistons that are interdigitated so that when one rotor rotates with respect to the other rotor, some chambers between the interdigitated pistons are reduced in volume and other chambers are increased in volume. Respective one-way bearings connect the first and second rotors to the main shaft to incrementally rotate it. Fuel mixture and exhaust apparatus is connected to one end of the engine to feed a fuel mixture to the increasing-volume chambers and extract the exhaust from other decreasing-volume chambers. At the same time, yet other chambers are experiencing compression and ignition cycles. An oil pump is driven by the first and second rotors for circulating a lubricant from a reservoir, through the engine parts to be lubricated and then back to the reservoir to cool the lubricant.