The mathematical problem of the evolution of the asteroidal and meteoritic mass distributions under collisional fragmentation is re-examined. A power law of index −5/3 is shown to be a good approximation to the asymptotic solution for the most massive bodies (i.e. the larger asteroids). For less massive bodies a power law of index about −1.8 is indicated, the precise value of the index depending on the exact mode of break-up assumed.