Previous theories for the transport of solutes through cell membrane pores have not considered the fact that the pore may be so small that the water and solute molecules cannot pass by each other. A theory has been developed in this paper for such a pore. Transfer of solute through the pore requires movement of the whole pore "plug". Relations are derived between the macroscopic permeability constants and the pore structure which are much more general and rigorous than any previous result. For example, the average number of water molecules per pore can be determined just from the values of the hydraulic and diffusive permeability of the whole membrane to water. This derivation does not require any assumptions about the pore shape or about the interactions of the water molecules with each other or with the pore walls. The theory is applied to the experimental data for the red blood cell. Although there is general agreement between the theory and experiment, there are some important discrepancies which are discussed. According to arguments given in detail in an appendix, it appears that there is a serious methodological error in the measurements made by Goldstein and Solomon (1960) (J. Gen. Physiol. 44, 1-17) of the red cell reflection coefficients and these values were not used when the theoretical and experimental results were compared.