Using Cassini ion neutral mass spectrometer stable isotope observations, we have developed a comprehensive method for modeling the time-evolution of the stable isotopic ratios in Titan's major constituents, N2, CH4 and H2. Our model provides constraints on the initial 14N/15N ratio in N2, the time scale for the outgassing of methane from the interior, and the initial D/H ratio in methane. Over geologic time scales, the isotopes are fractionated by diffusion, atmospheric escape and photochemistry. Diffusion and escape preferentially remove the lighter isotopes for all constituents. Photolysis of methane also removes the lighter isotopes, while photolysis of nitrogen preferentially removes the heavier isotopes. We have found the following: (1) even taking past hydrodynamic escape into consideration, the initial 14N/15N ratio in N2 cannot have changed much from its current value as the result of atmospheric processes. This is due to the large amount of N2 that must be fractionated. High-rate loss processes, such as hydrodynamic escape, are inefficient fractionators and take a very long time to change the isotopic ratio. On the other hand, low-rate loss processes are efficient fractionators, but also take a very long time to influence a large inventory. (2) The current inventory of methane represents the remnant of methane that, constrained by the 12C/13C ratio, began outgassing from the interior more than 60 million years ago, resulting in a total inventory of 3–4 times the current inventory cycling through the system during this time period. Methane production is likely to be ongoing. (3) The initial D/H in methane was found to be 6.96–11.3×10−5