Accurate and detailed models of the seismic velocity structure of gas hydrate-bearing sediments may be determined by careful analysis of controlled source seismic data. However, interpretation of these velocities in terms of hydrate saturation of the pore space has hitherto relied on semiempirical formulas and/or simple effective medium theory. We develop a rigorous theoretical scheme to relate the seismic properties of a clay-rich hydrate-bearing sediment to its porosity, mineralogy, microstructural features and hydrate saturation. We consider separately the two possible end-members for the distribution of hydrate in the pore space: (1) hydrates are unconnected and located in the pore voids without appreciable grain contact and (2) connected hydrates are forming cement binding around the grains. The scheme is transversely isotropic, to allow for anisotropy due to alignment of clay platelets, and is based on a combination of a self-consistent approximation, a differential effective medium theory, and a method of smoothing for crystalline aggregates. We have applied the scheme to lithological and seismic velocity data from Ocean Drilling Program Site 995 on the Blake Ridge (southeastern U.S. continental margin) to make estimates of the hydrate saturation. It was found that the hydrates are probably unconnected, and their volume concentration varies between ~0% at 100 m below the seabed and ~9% at 400 m depth, just above the bottom simulating reflector, if the clay platelet orientation distribution resembles the function we have used. ¿ 2000 American Geophysical Union