The present invention concerns an engine comprising at least one working cylinder (1) which has valves (16) and/or nozzles for the feed or injection of fuel and air and for the outlet of exhaust gas and a method of operating such an engine. In order to provide an engine and a corresponding method by which the fuel is used considerably more efficiently without excessively high temperatures occurring, which entail the risk of misfires, it is proposed according to the invention that each working cylinder (1) is coupled to a subsequent cylinder (11) which is driven by the pressure of hot exhaust gases from the working cylinder (1) and which is so designed and arranged that on the other hand it feeds pre-compressed combustion air to the working cylinder (1), a cooling device (17) which cools the pre-compressed gas, a device (9, 7) for transferring the cooled pre-compressed gas into the working cylinder (1) and a transfer valve (16) which for a further stroke of the subsequent cylinder (1) transfers exhaust gas under pressure from the working cylinder (1) into the subsequent cylinder (11).