A constant volume combustion system includes at least one combustion chamber having at least one admission port and an exhaust port. The system also includes at least one elastically deformable tongue made of ceramic matrix composite material forming an air admission valve, the tongue being present inside the chamber and being positioned facing the admission port, the tongue having a first end that is stationary relative to an inside wall of the chamber and a second end, opposite from the first end, the second end being free and movable relative to the inside wall.