Methane (CH4) concentration and stable isotope (δ2H-CH4 and δ13C-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? for δ2H-CH4 and 9? for δ13C-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 14C-CH4 show that the CH4 geochemistry in both basins is dominated (~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.