Abstract: A thermodynamic rotary engine (2) comprising a positive displacement compressor (4), a combustion chamber (6) in which air from the compressor and fuel are burnt, and a rotatable cyclicly operating gas expander (10) for receiving combustion gas from the combustion chamber, the gas expander comprising a rotor (12) which is constructed for rotation within a cylinder (16), the cylinder being rotatable with the rotor in the same direction as the rotor, the cylinder and the rotor defining between them a variable volume expansion chamber (10) as they rotate during operation of the engine, the cylinder having a fixed inwardly projecting vane (22) which slidably engages in sealing means (24) in the rotor and so divides the variable volume expansion chamber into two portions, the sealing means being rotatable in the rotor so that the vane can remain engaged between the rotor and the cylinder in spite of differential rotational speeds between the rotor and the cylinder during each cycle of operation of the gas expander