A rotary internal combustion engine which comprises a housing containing an axle, a pair of toroidal casings both containing a rotor with a piston disposed within the respective casings, an on/off valve for forming an ignition and explosion zone together with the piston disposed in the casings, and a gas outlet in the vicinity of the on/off valve disposed in the casings, whereby the rotation of the rotor within the internal combustion engine is achieved by transferring a compressed air-fuel mixture into the ignition and explosion zone, igniting the mixture and simultaneously, exploding, and exhausting the combusted gas through the gas outlet, thereby causing the rotation of the rotors together with the axle.