Abstract: This arrangement enables the identification of a plurality of vehicles (4) and determination of the instant of their passing over a reference line (30). It includes a moving station (1) mounted on the vehicle and a fixed station (2) arranged alongside a racetrack (3). The fixed station broadcasts a low-frequency synchronization signal of period T which is received by the moving station, the latter in turn broadcasting a series of signals of duration Tn located in a predetermined rank relative to the time t.sub.o marking each start of period T. Conjointly the moving station allocates an identification code peculiar to a given moving object to each signal Tn. The signals received by the fixed station are stored in a memory which for each signal memorizes its absolute time, its association with a given vehicle and its amplitude. The arrangement is used for motor vehicle races which include a large number of competitors.