Diffusion coefficients at infinite dilution are important basic data for all processes involving mass transfer. They can be obtained from studying samples in equilibrium using nuclear magnetic resonance spectroscopy with pulsed field gradients (PFG-NMR), a technique which is widely used in chemistry but is only rarely applied in engineering studies. This advantageous technique was employed here to measure the self-diffusion coefficients of diluted solutions of carbon dioxide and methane in the pure solvents water, ethanol, cyclohexane, toluene, methanol, and acetone at 298.15 K. For the systems (carbon dioxide + water) and (carbon dioxide + ethanol), measurements were also carried out at 308.15 K, 318.15 K and 333.15 K. Except for (methane + water) and (methane + toluene), no literature data for the methane-containing systems were previously available. At the studied solute concentrations, there is practically no difference between the self-diffusion coefficient and the mutual diffusion coefficient. The experimental results are compared to experimental literature data as well as to results from semi-empirical methods for the prediction of diffusion coefficients at infinite dilution. Furthermore, molecular dynamics simulations were carried out for all systems to determine the diffusion coefficient at infinite dilution based on