A rotary internal combustion engine comprising: an engine shaft ; at least first and second rotor assemblies each including: a housing having a rotor cavity and having an inlet port and an exhaust port in communication with the rotor cavity; and a rotor engaged to the engine shaft and received in the rotor cavity, the rotor cooperating with the housing to define plurality of combustion chambers in the rotor cavity, each of the combustion chambers having a respective working volume, an effective volumetric compression ratio determined by a first variation in the respective working volume during a compression phase of the combustion chamber and by a position of the inlet port , and an effective volumetric expansion ratio determined by a second variation in the respective working volume during an expansion phase of the combustion chamber and by a position of the exhaust port , wherein at least one of the combustion chambers of the first rotor assembly and at least one of the combustion chambers of the second rotor assembly have unequal effective volumetric compression ratios and/or unequal effective volumetric expansion ratios; characterised in that : an angular offset (α a ) between the inlet port of the first rotor assembly and a reference point (X) of the first rotor assembly is different from an angular offset (α b ) between the inlet port of the second rotor assembly and a corresponding reference point (X) of the second rotor assembly . an engine shaft ; at least first and second rotor assemblies each including: a housing having a rotor cavity and having an inlet port and an exhaust port in communication with the rotor cavity; and a rotor engaged to the engine shaft and received in the rotor cavity, the rotor cooperating with the housing to define plurality of combustion chambers in the rotor cavity, each of the combustion chambers having a respective working volume, an effective volumetric compression ratio determined by a first variation in the respective working volume during a compression phase of the combustion chamber and by a position of the inlet port , and an effective volumetric expansion ratio determined by a second variation in the respective working volume during an expansion phase of the combustion chamber and by a position of the exhaust port , wherein at least one of the combustion chambers of the first rotor assembly and at least one of the combustion chambers of the second rotor assembly have unequal effective volumetric compression ratios and/or unequal effective volumetric expansion ratios; a housing having a rotor cavity and having an inlet port and an exhaust port in communication with the rotor cavity; and a rotor engaged to the engine shaft and received in the rotor cavity, the rotor cooperating with the housing to define plurality of combustion chambers in the rotor cavity, each of the combustion chambers having a respective working volume, an effective volumetric compression ratio determined by a first variation in the respective working volume during a compression phase of the combustion chamber and by a position of the inlet port , and an effective volumetric expansion ratio determined by a second variation in the respective working volume during an expansion phase of the combustion chamber and by a position of the exhaust port , wherein at least one of the combustion chambers of the first rotor assembly and at least one of the combustion chambers of the second rotor assembly have unequal effective volumetric compression ratios and/or unequal effective volumetric expansion ratios; characterised in that : an angular offset (α a ) between the inlet port of the first rotor assembly and a reference point (X) of the first rotor assembly is different from an angular offset (α b ) between the inlet port of the second rotor assembly and a corresponding reference point (X) of the second rotor assembly . <EOS>