This invention relates to a rotary internal combustion engine that operates in a two-stroke cycle, equipped with a separate lubricating and/or cooling chamber. A rotary internal combustion engine consists of a rotor of which profile is two-lobed epitrochoid line, rotating on an eccentric shaft in a three-lobed engine body and the combination of a rotor and the body forms three working chambers with a phase difference of 120°. The air drawn into from the first chamber is compressed and scavenged into the second chamber through a gas conduit. The second chamber performs the functions of compression, ignition-expansion. The space in the third chamber is independent of the other two chambers, so the lubricant is fed to lubricate and cool the engine.