We describe first results from a numerical two-fluid MHD model of the global structure of the solar corona. The model is two-fluid in the sense that it accounts for the collisional energy exchange between protons and electrons. As in our single-fluid model, volumetric heat and momentum sources are required to produce high speed wind from coronal holes, low speed wind above streamers, and mass fluxes similar to the empirical solar wind. By specifying different proton and electron heating functions we obtain a high proton temperature in the coronal hole and a relatively low proton temperature above the streamer (in comparison with the electron temperature). This is consistent with inferences from SOHO/UltraViolet Coronagraph Spectrometer instrument (UVCS) [Kohl et al., 1997>, and with the Ulysses/Solar Wind Observations Over the Poles of the Sun instrument (SWOOPS) proton and electron temperature measurements which we show from the fast latitude scan. The density in the coronal hole between 2 and 5 solar radii (2 and 5RS) is similar to the density reported from SPARTAN 201-01 measurements by Fisher and Guhathakurta [1994>. The proton mass flux scaled to 1 AU is 2.4¿108 cm-2 s-1, which is consistent with Ulysses observations [Phillips et al., 1995>. Inside the closed field region, the density is sufficiently high so that the simulation gives equal proton and electron temperatures due to the high collision rate. In open field regions (in the coronal hole and above the streamer) the proton and electron temperatures differ by varying amounts. In the streamer the temperature and density are similar to those reported empirically by Li et al. [1998>, and the plasma &bgr; is larger than unity everywhere above ~1.5RS, as it is in all other MHD coronal streamer models [e.g., Steinolfson et al., 1982; also G. A. Gary and D. Alexander, Constructing the coronal magnetic field, submitted to Solar Physics, 1998>. ¿ 1999 American Geophysical Union