A chemical oxidation scheme where CH3D produces HDO has been incorporated into a two-dimensional model to simulate the transport and isotopic composition chemistry of stratospheric methane and water. The model results show that deuterium ratios in water and methane are good tracers of stratospheric dynamics. Comparisons with measurements by the ATMOS instrument suggest that the modeled methane isotopic ratio is too low in the upper stratosphere and mesosphere. The very low amount of CH4 and CH3D in the middle to upper stratosphere makes the isotopic ratio for methane more sensitive to model uncertainties than the isotopic ratio of water vapor. One reason for the too low isotopic ratio values may be that the reaction rates in the oxidation of CH3D are slower than assumed. The isotopic ratio for methane was very sensitive to changes in the rate constants for the reactions of CH3D with OH, O(1D) and Cl, while the water vapor isotopic ratio only shows small changes.