The device comprises two heat exchangers (74, 90) suitable respectively for vaporizing first and second propellants before they are reintroduced in gaseous form into their tanks (16, 18). The heat exchangers co-operate respectively with first and second gas generators (60, 84) suitable for being fed with a mixture of propellants in order to produce combustion, the second gas generator (84) being suitable for being fed at least in part by the exhaust from the first gas generator (60).