Recently, it was shown(1,2) that the diffusion coefficient and nuclear magnetic resonance (NMR) relaxation times of a molecule in a mixture of alkanes follow scaling laws in the chain length of the molecule and the mean chain length of the mixture. These relations can be used to determine the chain length distribution of crude oils from diffusion and relaxation measurements. Oil reservoirs are Usually at elevated temperatures and pressures, so it is important to know how these scaling relations depend on temperature and pressure. In this paper, we obtain the relation between the molecular composition of mixtures of alkanes at elevated pressures and temperatures and their diffusion coefficients D-i and relaxation times T-1i and T-2i. Using proper-ties of free volume theory and the behavior of the density of alkanes, we show that, for a large range of pressures, the diffusion coefficients and relaxation times depend on pressure and mean chain length of the Mixture only through its density. We further show that the pressure effect can be taken into account in the power laws of refs 1 and 2 by a multiplicative prefactor that depends only on temperature and the free volumes of pure alkanes at the pressure of interest and a reference pressure. We also combine the scaling laws for D-i, T-1i, and T-2i and the Arrhenius dependence on temperature to obtain the temperature dependence of the diffusion coefficients and relaxation times. We obtain good fits between the scaling relations and literature data. These scaling relations can be used to determine the composition of a mixture of alkanes from measurements of diffusion coefficients or relaxation times at elevated pressures and temperatures.