The existence of a small intrinsic magnetic field at Mars is still being debated. The ion densities, measured in the Martian ionosphere above 300 km by the retarding potential analyzers on the Viking landers, are very low (Hanson et al., 1977). The ionospheric thermal pressure above 300 km is insufficient by itself to withstand the solar wind dynamic pressure, suggesting the presence of a magnetic field in the ionosphere of Mars (Hanson and Mantas, 1988). However, two types of ionospheric magnetic field in the ionosphere of Mars (Hanson and Mantas, 1988). However, two types of ionospheric magnetic field are possible: (1) a weak intrinsic magnetic field, or (2) an induced magnetic field driven by the solar wind interaction with Mars. The latter situation is analogous to the Venus ionosphere during conditions of high solar wind dynanic pressure. It has been pointed out that the measured plasma scale heights and temperatures for the Martian ionosphere are very similar to those observed in the Venus ionosphere during conditions of large solar wind dynamic pressure (Luhmann et al., 1987). We present a one-dimensional, multispecies, magnetohydrodynamic model of the Martian ionosphere. Scenarios with and without a small intrinsic field are modeled for Viking conditions (solar minimum). We find that the calculated ion density profiles are not in better agreement with measured ones if an intrinsic magnetic field is included in the model. The results also indicate that large horizontal plasma motions must be present at high altitudes, which implies that the dynamics of the upper ionosphere of Mars is controlled by the solar wind. ¿ American Geophysical Union 1989