The rotary nasal annular engine with noses on the annular with internal combustion operates on the principle of a pair of the first rotor (1) and the second rotor (2), as well as with usage of a block (3), where the rotors are placed and rotate synchronously. The block (3), together with the circumference surface (1.9), nose (1.2), (1.3) of the rotor (1) and the rotor (2) determinates the engine's combustion chamber (4.1), (4.2) in the shape of a torus, inside of which the rotor (1) is rotating with at least one nose (1.2). The rotor (2), contains, on its outer circumference surface (2.9), slots (2.7, 2.8), preferably, on its outer circumference surface, for the transition of the nose (1.2). During the nose's (1.2) transition through the slot (2.7), of the rotor (2), the compressed medium (7) is transferred through the storage system (2.5) of the rotor (2) through its intake opening (2.4) of the rotor (2) and through the outgoing opening (2.6) of the rotor (2) into the engine's combustion chamber (4.2)