A rocket propulsion system comprises a combustion chamber, an oxygen supply system, comprising an oxygen supply duct and being configured to supply oxygen to the combustion chamber, and a hydrogen supply system, comprising a hydrogen supply duct and being configured to supply hydrogen to the combustion chamber. An ignition unit of the propulsion system, to which at least portions of the oxygen and the hydrogen supplied to the combustion chamber can be supplied, is configured to initiate combustion of the oxygen-hydrogen mixture in the combustion chamber. The propulsion system further comprises a cooling duct extending along an inner surface of a combustion chamber wall and through which at least a portion of the oxygen supplied to the combustion chamber, at least a portion of the hydrogen supplied to the combustion chamber or a combustion gas mixture emerging from the ignition unit flows.