The engine (10) has a compressor (12) for compressing air, a plurality of combustion chambers (22a f) in which fuel mixed with the compressed air combusts, and a turbine (16) which is driven by the products of combustion. Each combustion chamber operates in a cycle comprising the phases of: A. charging the combustion chamber with a charge of compressed air from the compressor while preventing air from escaping from the combustion chamber; B. then compounding by charging with a compounding charge of gas to form a compounded charge; C. then injecting fuel into the combustion chamber so that there is spontaneous ignition and combustion of the fuel with the compounded charge; and D. then exhausting the products of combustion to the turbine. The cycles of the combustion chambers are out of phase in a sequence, and part of the compounded charge (and/or the products of combustion thereof) in each combustion chamber during the combustion phase thereof is transferred to the next combustion chamber in the sequence to provide the compounding charge for that next combustion chamber.
