Method for the operation of a weapon system, which contains both a weapon with a height-adjustable barrel and a fire control computer and, with the weapon in the loaded state, includes ammunition programmable by the fire control computer, wherein the ammunition contains a warhead in the form of an explosive device with a programmable detonator, which is detonated according to its programming after firing of the ammunition at a spatially predetermined air blast point (12, 14) in relation to a moving target, with the characteristics: a. in order to determine the trajectory and the arming time of the warhead, in addition to the measurements of the target distance (L o) and the firing range, the velocity component of the target directed towards the weapon is also determined as the target longitudinal velocity (v z), b. in order to determine the velocity component of the target directed towards the weapon at least two consecutive distance measurements are carried out between the weapon and the moving target and the target longitudinal velocity (v z) of the target is determined from the difference and the time interval between the determination measurements, c. the corrected trajectory and the arming time of the warhead are determined by the fire control computer by extrapolation, taking into account the target, the initial target distance (L o), the flight time of the warhead which is associated with the ammunition and the determined target longitudinal velocity (v z) of the target, wherein d. the extrapolated target distance results from the initial target distance (L o) and the target movement calculated from the flight time of the warhead associated with the ammunition times the target longitudinal velocity (v z) of the target, e. and then the barrel is oriented with respect to its elevation and the detonator of the warhead is programmed with respect to the arming time. a. in order to determine the trajectory and the arming time of the warhead, in addition to the measurements of the target distance (L o) and the firing range, the velocity component of the target directed towards the weapon is also determined as the target longitudinal velocity (v z), b. in order to determine the velocity component of the target directed towards the weapon at least two consecutive distance measurements are carried out between the weapon and the moving target and the target longitudinal velocity (v z) of the target is determined from the difference and the time interval between the determination measurements, c. the corrected trajectory and the arming time of the warhead are determined by the fire control computer by extrapolation, taking into account the target, the initial target distance (L o), the flight time of the warhead which is associated with the ammunition and the determined target longitudinal velocity (v z) of the target, wherein d. the extrapolated target distance results from the initial target distance (L o) and the target movement calculated from the flight time of the warhead associated with the ammunition times the target longitudinal velocity (v z) of the target, e. and then the barrel is oriented with respect to its elevation and the detonator of the warhead is programmed with respect to the arming time.