In this paper, grain-grain collisions, which were recently suggested by Biermann and Harwit (1980) to occur in cool circumstellar envelopes and to be responsible for the interstellar grain size spectrum, are investigated. On the basis of the author's fragmentation theory, it is shown that in the result of such collisions size distributions of the typen(a) ρa−p arise. In the steady-state case the exponentp ranges from 3.4 to 3.7. This result matches well with grain size spectra derived from the interstellar extinction curve.