A study of the use of millimeter-wavelength spectral transitions to investigate the atmosphere of Mars is presented. In the model experiments investigated it is assumed that a spectrometer in the frequency range from 100 to 260 GHz looks into a modest-sized telescope of from 30 to 50 cm aperture from a near-Mars orbit. The molecules H(2)O, CO, O(2), O(3), and H(2)O(2) all have intense spectral lines in the Mars atmosphere in this frequency range and in addition are all very important in understanding the water cycle, the photochemistry, and the circularization in that atmosphere. It is shown that the altitude and the zonal distribution of H(2)O can be mapped even in atmospheric columns as dry as 0.25 precipital µm. Ozone can be mapped over the entire planet, independent of solar-lighting conditions, dust loading, or clouds in the atmosphere, because millimeter waves are insensitive to any particles that can be suspended in the Mars atmosphere. Because the signal-receiving techniques use superheterodyne devices and narrow spectral lines, zonal and meridional winds can be measured at altitudes above 10 km with a precision approaching approximately 3 m/s by the use of Doppler shifts. Temperature-pressure profiles can be measured to altitudes of 100 km by the use of CO lines in the limb-sounding mode.