The pressure and temperature dependent thermal conductivity k of Al2O3 and MgO is determined for mantle and core conditions. We model the pressure dependence by relating k to compression, either linearly or with a power law relationship; we assume k is inversely proportional to temperature as expected in nonmetals at temperatures greater than a few hundred Kelvin. In order to determine model parameters, we use experimental data collected in the laser-heated diamond-anvil cell at pressures of 58 and 125 GPa, combined with a model for heat transfer in the diamond cell. The thermal conductivities predicted by the two models differ by less than 30% and are in good agreement with results obtained from independent shock experiments. Throughout the lower mantle we find that k~5--12 W/mK, consistent with geodynamical constraints and previous theoretical estimates, and is nearly constant along an adiabat.¿ 1997 American Geophysical Union