a preparatory stage using the deterioration curve co overall damage epc 2 is established due to use of the second power during an accumulated time interval tc 2 this overall damage being equal to the product of the accumulated second time interval multiplied by the targeted deterioration coefficient as determined with the help of the deterioration curve by using the value of the monitoring parameter reached while the engine is developing the second power furthermore excursions at third powers lying between the first power and the second power are discrete and they are numbered using an index i the intermediate damage generated during each excursion of an intermediate duration di is equal to each intermediate damage ei is established and stored during the flight by the determination means 3 under such circumstances at each current use of the third power taking place after earlier excursions that have caused intermediate damage to be stored in memory the determination means 3 establish and store the current deterioration coefficient of the engine and then determine a third duration of utilization u03b4t u2033 at each current instant using the following relationship u03b4 u2062 u2062 t u2033 epc u2062 u2062 2 u2211 i 1 n 1 u2062 ei u222b.