Desorption profiles of trichloroethylene (TCE), tetrachloroethylene (PCE), and a TCE-PCE mixture were measured for three natural solids and four zeolites. Initial sorbed mass (Mi) in slow desorbing sites of natural solids and in micropores of zeolites were obtained from desorption profiles. In natural solids, Mi increases with recalcitrant organic matter content. In zeolites, Mi generally increases with decreasing micropore width and increasing micropore hydrophobicity, but the effect of hydrophobicity is stronger. In both natural solids and zeolites, competition between TCE and PCE causes Mi for each sorbate in the mixture to be less than or similar to that for each sorbate alone. Zeolite results indicate that micropore width affects this competition more than micropore hydrophobicity for the solids examined. Desorption in all solids was simulated with the radial diffusion model, either alone or coupled with the advection-dispersion equation when necessary; diffusion rate constants (D/R2) were obtained. In natural solids, mean values of D/R2 increase with decreasing recalcitrant organic matter content. In zeolites, values of D/R2 generally increase with increasing micropore width, while they are a weak function of hydrophobicity. In both natural solids and zeolites, competition between TCE and PCE causes D/R2 for each sorbate in the mixture to generally be larger than that for each sorbate alone. Zeolite results indicate that the effects of competition on D/R2 generally decrease with decreasing micropore width for the solids examined; a trend with micropore hydrophobicity is not apparent. For the three natural solids and four zeolites examined in this study, the similar effects of competition between TCE and PCE on values of Mi and D/R2 and the overlapping range of D/R2 values support the hypothesis that diffusion through hydrophobic micropores affects and may control slow mass transfer processes in the recalcitrant organic matter of natural solids. These results contribute to the fundamental understanding of slow mass transfer processes in natural solids, and they indicate that characterization of micropore width and polarity may be necessary to predict organic chemical transport and fate.