Abstract: An internal combustion rotor-piston engine has a main body embedding two intersecting torus-like cavities. Each cavity guides two arc-shaped pistons. A main driving shaft has a central spherical part allocating four slots under a certain angle with the axis of the main driving shaft. Each of the four pistons has two butt-end surfaces and is connected with the main driving shaft by four coupling devices with an arc-shaped sector moving along the corresponding slot on the spherical part of the main driving shaft and a pin extending into the piston, for transmitting torque to the main driving shaft. The internal combustion rotor-piston engine further has a common outlet window for the two intersecting cavities and a common outlet window for the two intersecting cavities joining an outlet pipe. Each piston has a built-in chamber of combustion on the rear part thereof.