Anisotropic diffusion was studied in Opalinus Clay, a potential host rock for disposal of spent fuel, vitrified high-level waste, and long-lived intermediate-level waste in Switzerland. Diffusion parallel to the bedding was measured using a radial through-diffusion technique and diffusion perpendicular to the bedding bythe classical (planar) through-diffusion technique. The samples used were from Mont Terri (MT) and from Benken (BE). Diffusion of HTO, 36Cl-, and 22Na+ parallel and perpendicular to the bedding was studied under confining pressures of 7 MPa (MT) and 14 MPa (BE). The results indicate that diffusion parallel to the bedding is faster than diffusion perpendicular to the bedding by a factor of 4-6 for the three radionuclides, indicating that the Opalinus Clay is anisotropic. This might be explained by smaller path lengths (tortuosity) for species diffusing parallel to the fabric. The degree of anisotropy is slightly smaller for Opalinus Clay from Mont Terri than from Benken. This is due to the lower overburden pressure in Mont Terri resulting in a lower preferential orientation of the clay platelets.