Abstract: A rotary internal combustion engine comprises a rotor assembly which is mounted to rotate about an axis of rotation and comprises a double-headed piston member having two primary pistons at opposite ends respectively of an intermediate portion of the piston member and also having two secondary pistons at opposite ends respectively of the intermediate portion, and a double-headed cylinder member defining two primary cylinders in which the two primary pistons are fitted respectively and also defining two secondary cylinders in which the two secondary pistons are fitted respectively. One of the members is mounted to rotate about the axis of rotation of the rotor assembly, while the other member rotates about a crank axis which is offset from the axis of rotation of the rotor assembly. Thus, the pistons reciprocate relative to the cylinders as the rotor assembly rotates.