Voyager 2 images of the Neptunian ring system show it to be relatively dusty with the fraction of micro-sized dust particles in the rings between the 0.2 and 0.7 (Smith et al. 1989). We apply a numerical model developed for the Uranus dust bands [Colwell and Esposito, Icarus, (in press)> to the Neptune system. Our results show that 1) the suggested bimodal distribution of dust fractions in the rings is not related to ring optical depth and may be due to different ring particle size distributions. 2) Collision velocities between the macroscopic ring particles must be ~1 m/sec if they are to produce dust fractions above 1/2. 3) The small moons of Neptune must have regoliths for meteoroid excavation to produce the dust population at Voyager ring plane crossing. 4) Dust optical depths interior to 1989N3R are negligible unless there are unseen macroscopic source bodies in that region. ¿The American Geophysical Union 1990