Method of managing a power demand P D to assure the operation of a pilotless aircraft, implemented by appropriate software in a propulsion control unit of the aircraft, said aircraft including an internal combustion engine supplying a maximum principal power P M liable to vary, characterized in that, in the absence of failure of said internal combustion engine, the following steps are carried out: a) collecting at least some of the exhaust gases when this internal combustion engine is operating, b) feeding a turbine with the energy of the gases collected in this way, c) producing an electrical current by means of an electrical generator connected to said turbine, and d) comparing the maximum principal power P M supplied by said internal combustion engine at the time of the power demand with the demanded power P D, e) if the maximum principal power P M is at least equal to the demanded power P D, storing at least some of the electrical energy generated in this way in at least one energy storage unit and/or using at least some of the electrical energy generated in this way to assist the internal combustion engine by supplying an auxiliary power P A complementing a main power P t developed by the internal combustion engine, with P t less than P M, so that P A + P t = P D, or f) if the maximum principal power P M is less than the power P D demanded for the operation of said aircraft, using at least some of the electrical energy generated in this way to assist the internal combustion engine to provide the demanded power P D or using at least some of the electrical energy stored in said at least one energy storage unit to assist the internal combustion engine to supply the demanded power P D, or g) if the demanded power P D is greater than the sum of the maximum principal power P M developed by the internal combustion engine and the auxiliary power that can be supplied by said at least one storage unit, modifying the operation of said aircraft so as to be able to supply said demanded power P D in accordance with one of the steps e) or f). a) collecting at least some of the exhaust gases when this internal combustion engine is operating, b) feeding a turbine with the energy of the gases collected in this way, c) producing an electrical current by means of an electrical generator connected to said turbine, and d) comparing the maximum principal power P M supplied by said internal combustion engine at the time of the power demand with the demanded power P D, e) if the maximum principal power P M is at least equal to the demanded power P D, storing at least some of the electrical energy generated in this way in at least one energy storage unit and/or using at least some of the electrical energy generated in this way to assist the internal combustion engine by supplying an auxiliary power P A complementing a main power P t developed by the internal combustion engine, with P t less than P M, so that P A + P t = P D, or f) if the maximum principal power P M is less than the power P D demanded for the operation of said aircraft, using at least some of the electrical energy generated in this way to assist the internal combustion engine to provide the demanded power P D or using at least some of the electrical energy stored in said at least one energy storage unit to assist the internal combustion engine to supply the demanded power P D, or g) if the demanded power P D is greater than the sum of the maximum principal power P M developed by the internal combustion engine and the auxiliary power that can be supplied by said at least one storage unit, modifying the operation of said aircraft so as to be able to supply said demanded power P D in accordance with one of the steps e) or f).