In-situ synchrotron X-ray computed microtomography with sub-micrometer voxel size was used to study the decomposition of gas hydrates in a sedimentary matrix. Xenon-hydrate was used instead of methane hydrate to enhance the absorption contrast. The microstructural features of the decomposition process were elucidated indicating that the decomposition starts at the hydrate-gas interface; it does not proceed at the contacts with quartz grains. Melt water accumulates at retreating hydrate surface. The decomposition is not homogeneous and the decomposition rates depend on the distance of the hydrate surface to the gas phase indicating a diffusion-limitation of the gas transport through the water phase. Gas is found to be metastably enriched in the water phase with a concentration decreasing away from the hydrate-water interface. The initial decomposition process facilitates redistribution of fluid phases in the pore space and local reformation of gas hydrates. The observations allow also rationalizing earlier conjectures from experiments with low spatial resolutions and suggest that the hydrate-sediment assemblies remain intact until the hydrate spacers between sediment grains finally collapse; possible effects on mechanical stability and permeability are discussed. The resulting time resolved characteristics of gas hydrate decomposition and the influence of melt water on the reaction rate are of importance for a suggested gas recovery from marine sediments by depressurization.