We have investigated the transport properties of nanopore alumina membranes that were rendered hydrophobic by functionalization with octadecyltrimethoxysilane (ODS). The pores in these ODS-modified membranes are so hydrophobic that they are not wetted by water. Nevertheless, nonionic molecules can be transported from an aqueous feed solution on one side of the membrane, through the dry nanopores, and into an aqueous receiver solution on the other side. The transport mechanism involves Langmuir-type adsorption of the permeating molecule onto the ODS layers lining the pore walls, followed by solid-state diffusion along these ODS layers; we have measured the diffusion coefficients associated with this transport process. We have also investigated the transport properties of membranes prepared by filling the ODS-modified pores with the water-immiscible (hydrophobic) liquid mineral oil. In this case the transport mechanism involves solvent extraction of the permeating molecule into the mineral oil subphase confined with the pores, followed by solution-based diffusion through this liquid subphase. Because of this different transport mechanism, the supported-liquid membranes show substantially better transport selectivity than the ODS-modified membranes that contain no liquid subphase.