The occultation of Epsilon Geminorum by Mars on April 8, 1976, was observed at three wavelengths and 4-ms time resolution with the 91-cm telescope aboard NASA's G. P. Kuiper Airborne Observatory. Temperature, pressure, and number-density profiles of the Martian atmosphere were obtained for both the immersion and emersion events. Within the altitude range 50-80 km above the mean surface, the mean temperature is about 145 K, and the profiles exhibit wavelike structures with a peak-to-peak amplitude of 35 K and a vertical scale of about 20 km. The ratio of the refractivity of the atmosphere at 4500 A and 7500 A is consistent with the atmospheric composition measured by Viking 1. From the 'central flash' - a bright feature in the light curve midway between immersion and emersion - an optical depth at 4500 A of 3.3 + or - 1.7 per km atm (about 0.23 per equivalent Martian air mass) is found for the atmosphere about 25 km above the mean surface near the south polar region. This large value and its weak wavelength dependence rule out Rayleigh scattering as the principal cause of the observed extinction.