A distinct fluid description for neutral hydrogen originating from either the interstellar medium, the heliosheath, or the solar wind has been developed to describe the detailed interaction of the solar wind with the local interstellar medium (LISM) [Williams et al., 1995>. Such a multifluid description for the hydrogen serves to capture the highly anisotropic nature of the neutral distribution. The neutral multifluid is coupled to a hydrodynamic plasma through charge exchange and the time-dependent model is solved in two spatial dimensions. This approach is used (1) to elucidate the nature of the solar wind - LISM interaction more carefully and precisely than has been done previously; (2) to identify precisely the role played by the three identifiably distinct neutral populations in determining the global structure and dynamics of the heliosphere (it is found, for example, that the heliopause is weakly time-dependent for the two-shock model); (3) to contrast these results with those obtained from the simpler, computationally more efficient model developed by Pauls et al. [1995>; and (4) to investigate the differences in global heliospheric structure and neutral properties between a two-shock (which results from a supersonic interstellar wind impinging on the heliosphere) and a one-shock (i.e., for a subsonic interstellar wind) model. In particular, observational criteria are presented that may allow one to distinguish between a one-shock and a two-shock heliosphere. ¿ American Geophysical Union 1996