Escape of neutral hydrogen (H) and nitrogen (N) from Triton maintains a large neutral cloud, called the Triton torus, in Neptune's magnetosphere. We have developed the first detailed Monte Carlo simulation model of the Triton torus that includes the collisionality, the complex geometry, the injection of two neutral species from Triton (H and N), and the combined effects of photoionization, electron impact ionization, and charge exchange. Ionization in Neptune's plasma sheet was modeled using Voyager plasma observations. Collisions cause both the H and N neutral clouds to become more radially extended, both toward Neptune and out beyond the magnetopause, as well as more extended in latitude, when compared with collisionless models. Moreover, collisions of H with the much more massive N greatly enhance the collisional ejection of H from the system and into Neptune's atmosphere. This effect decreases the probability of H ionization within the magnetosphere relative to that for N, and furthermore causes model results for two-species injection from Triton to differ significantly from those for H injection alone. For a hydrogen escape rate from Triton of 5¿1025 s-1, as given by photochemical models of Triton's upper atmosphere, a nitrogen excape rate of 5¿1024 s-1 gives proton and N+ sources of 5.6¿1024 s-1 and 3.3¿1024 s-1, respectively, whose ratio is close to the observer ratio of protons to heavies. A nitrogen escape rate of 2¿1025 s-1, for the same hydrogen escape rate of 5¿1025 s-1, yields an N+ source more than twice that of protons, inconsistent with the Voyager data. ¿ American Geophysical Union 1994