The basic theory of the accretion process, while applicable to planets generally, is applied here to the asteroids as examples The approach velocity among early asteroidal particles in the solar nebula is estimated to be of the order 1 X 10~ cm/sec. Asteroids could grow to observed radii in this case in 108 years, assuming efficient sticking (earliest growth may have been by another, non-accretionary process). The overabundance of the largest asteroids (d> 300 km) is attributed to two factors: the capture cross- section begins to rise steeply at diameter about 140 km, and the asteroids become stable against mass loss by even the highest-velocity impacts at diameter roughly 350 km. Larger bodies would grow rapidly, accounting for the apparent overabundance of large asteroids It is suggested that the mass distribution reconstructed by Anders, with the three largest asteroids overabundant, was "frozen" when the growth process was interrupted, perhaps by disruption of the solar nebula. Approach velocities have increased since the formation of the planets to the present value of a few km/sec, and consequently asteroids smaller than about 300-km diameter have eroded during most of solar-system history