The lattice parameters of synthetic diaspore (AlO(OH)) and synthetic and natural corundum (Al2O3) have been measured at simultaneously elevated pressure and temperature up to 7 GPa and 800 degreesC (1000 degreesC for corundum) using a MAX 80 cubic anvil high-pressure apparatus. Several experimental runs were carried out for both minerals, in which the samples were first compressed at room temperature and then heated; NaCl served as an internal standard for pressure calibration. In most runs the samples were mixed with Vaseline or NaCl to ensure hydrostatic pressure-transmitting conditions. Some runs, mainly at pressures < 4 GPa, were performed without using a pressure medium. A Birch-Murnaghan equation of state (EOS) was fitted to the experimental data obtained at room temperature (assuming K' = 4), yielding bulk moduli K (diaspore) = 134.4+/-1.4 GPa in contrast to 230 GPa obtained from diamond anvil cell measurements without using a pressure medium recently, and K (corundum) = 219.1+/-3.5 GPa, consistent with previous results based on X-ray diffraction measurements in conjunction with multi-anvil high-pressure techniques. The high-temperature Birch-Murnaghan EOS was fitted to the high-temperature high-pressure diaspore data, P = 1.5 K-T [V-T,r(-7) - V-T,r(-5)] [1 - 0.75 (4 - K'(T)) (V-T,r(-2) - 1)], V-T,V-r = (V/V-T,V-0)(1/3), K-T = K + (partial derivativeK(T)/partial derivativeT)(P) (T - 298.15), V-T,V-0 = 1 17.84 Angstrom (3) exp (integrala + bT dT), resulting in K = 133.6+/-4.0 GPa, K-T' = 4.1+/-1.5, (partial derivativeK(T)/partial derivativeT)(P) = 0.017+/-0.007 GPa K-1, a = 2.22+/-0.40 10(-5) K-1, and b = 2.23+/-0.79 10(-8) K-2.