We have undertaken a kinetic study of heterogeneous ozone decomposition on alpha-Fe2O3 (hematite) and alpha-Al2O3 (corundum) aerosols under ambient conditions of temperature, pressure, and relative humidity in order to better understand the role of mineral dust aerosol in ozone loss mechanisms in the atmosphere. The kinetic measurements are made in an environmental aerosol reaction chamber by use of infrared and ultraviolet spectroscopic probes. The apparent heterogeneous uptake coefficient, gamma, for ozone reaction with alpha-Fe2O3 and alpha-Al2O3 surfaces is determined as a function of relative humidity (RH). The uptake of ozone by the iron oxide surface is approximately an order of magnitude larger than that by the aluminum oxide sample, under dry conditions. At the pressures used, alpha-Fe2O3 shows clear evidence for catalytic decomposition of ozone while alpha-Al2O3 appears to saturate at a finite ozone coverage. The measured uptake for both minerals decreases markedly as the RH is increased. Comparison with other literature reports and the atmospheric implications of these results are discussed.