Collisional evolution of the mass-distribution spectrum of planetesimals. IIAn investigation of conditions for the early growth of planetesimals through their mutual collisions using Monte Carlo technique is presented. Rebound, erosion, catastrophic breakup, and coagulation are considered, mean random velocity is assumed to vary with time, and growth of km-sized planetesimals is shown to occur only when they have the mechanical properties similar to iron meteorites. The formation time of several hundred-km sized planetesimals is much longer than previously reported by Greenberg (1978), and an expression was derived for the temporal variation of the mean mass.