This paper discusses migration of radionuclides in the bedrock surrounding a repository. Currently available models use either a surface reaction or a bulk reaction concept to describe the retardation of migrating nuclides. The first model assumes that the nuclide reacts only with the surface of the fissures. This implies that the rock matrix is not utilized as a sink. The other model implies that the whole bulk of the rock is accessible to the nuclides. The paper analyzes the accessibility of the rock matrix to the radionuclides. The transport mechanisms are shown to be flow of water and nuclides in the fissures and transport of nuclides from the water in the fissures into water in the microfissures of the rock by pore diffusion. The diffusion of the nuclides into the rock matrix and their sorption onto the surfaces of the microfissures are the main mechanisms retarding migration from a repository. The diffusivity of the nuclide may be as important as its sorption equilibrium constant. Diffusivities in the pores and microfissures in such dense rocks as granite under confining pressure of hundreds of bars can be expected to be 6--20% of the diffusivity in water. These data are obtained from electrical resistivity measurements of salt-water-filled granites. Porosity of such granites varies from 0.4 to 0.9%. The apparent diffusivities in the granites well then vary between 0.25⋅10-12/Kd&rgr;p m2/s, where Kd&rgr;p is the volume equilibrium constant. This varies from the porosity of the rock for nonsorbing species to up to and over 104. For a 100-year contact time a nonsorbing nuclide can be expected to penetrate tens of meters of the rock matrix and a strongly sorbing nuclide with Kd&rgr;p larger than 104 will penetrate a few millimeters. The diffusion into the rock matrix can enhance the retardation by many orders of magnitude as compared to retardation by surface reaction in fissures only. The retardation may, on the other hand, be many orders of magnitude smaller than the maximum, value that could be obtained if all the rock matrix were accessible. This depends very much on the fissure widths and spacings.