Methane (CH4) concentration and stable isotope (delta H-2-CH4 and delta C-13-CH4) depth distributions show large differences in the water columns of the Earth's largest CH4-containing anoxic basins, the Black Sea and Cariaco Basin. In the deep basins, the between-basin stable isotope differences are large, 83 parts per thousand for delta H-2-CH4 and 9 parts per thousand for delta C-13-CH4, and the distributions are mirror images of one another. The major sink in both basins, anaerobic oxidation of CH4, results in such extensive isotope fractionation that little direct information can be obtained regarding sources. Recent measurements of natural C-14-CH4 show that the CH4 geochemistry in both basins is dominated (similar to 64 to 98%) by inputs of fossil ( radiocarbon-free) CH4 from seafloor seeps. We derive open-system kinetic isotope effect equations and use a one-dimensional (vertical) stable isotope box model that, along with isotope budgets developed using radiocarbon, permits a quantitative treatment of the stable isotope differences. We show that two main factors control the CH4 concentration and stable isotope differences: (1) the depth distributions of the input of CH4 from seafloor seeps and (2) anaerobic oxidation of CH4 under open-system steady state conditions in the Black Sea and open-system non-steady-state conditions in the Cariaco Basin.