Results of a fully three-dimensional model of the interaction of the solar wind with the local interstellar medium are presented. The effects of charge-exchange with interstellar neutral hydrogen are taken into account self-consistently, while the effects of hot solar wind neutral hydrogen, as well as cosmic rays and magnetic fields, are ignored in this study. In accord with solar medium observations by Ulysses, the solar wind is assumed to depend on heliolatitude. Two large, long-lived polar coronal holes, one in the northern hemisphere and the other in the southern hemisphere, are assumed to produce a hot, low-density, high-speed wind which bounds a cooler, higher-density, low-speed ecliptic wind. The solar wind boundary conditions, which allow for a 1.5 increase in solar wind ram pressure over the poles of the Sun compared with the ecliptic plane, are drawn from published Ulysses data [Phillips et al., 1995, 1996>. The results of this simulation are compared with the no-charge-exchange asymmetric solar wind simulation, described by Pauls and Zank [1996>. It is found that the elongation of the heliosphere along the solar poles, resulting from the ram pressure increase with heliolatitude, induces a greater influx of interstellar hydrogen over the poles of the Sun than in the ecliptic plane. This, in turn, reduces the extent of elongation of the heliosphere along the poles of the Sun. The vorticity, found in the no-charge-exchange simulation, is absent in the presence of charge-exchange. Once again, as found by Baranov and Malama [1993> and Pauls et al. [1995>, the interaction of the solar wind with the local interstellar medium is influenced strongly by charge-exchange processes.¿ 1997 American Geophysical Union