The nightside ionosphere of Mars could be produced by electron precipitation or by plasma transport from the dayside, by analogy to the Venus, but few measurements are available. We report here model calculations of upper limits to the nightside ion densities on Mars that would be produced by both mechanisms. For the auroral model, we have adopted the downward traveling portions of the electron spectra measured by the HARP instrument on the Soviet Phobos spacecraft in the Martian plasma sheet and in the magnetotail lobes. For the plasma transport case, we have imposed on a model of the nightside thermosphere, downward fluxes of O+, C+, N+, NO+, and O2+ that are near the maximum upward fluxes that can be sustained by the dayside ionosphere. The computed electron density peaks are in the range (1.3-1.9)¿104 cm-3 at altitudes of 159 to 179 km. The major ion for all the models is O2+, but significant differences in the composition of the minor ions are found for the ionospheres produced by auroral precipitation and by plasma transport. The calculations reported here provide a guide to the data that should be acquired during a future aeronomy mission to Mars, in order to determine the sources of the nightside ionosphere. ¿ American Geophysical Union 1993