The theory of the isotopic exchange of 2H and 3H between an enzyme-substrate complex and the solvent is derived for 16 different types of experiment involving measurements of initial velocities and of the isotopic content of the reactants and products as a function of the extent of reaction. It is shown how the data from these experiments can be analyzed to obtain the rate constants for the individual steps and thereby the Gibbs free energies of the intermediates and transition states in the reaction. The effects of isotopic substitution on each intermediate and transition state are also found and this allows conclusions to be drawn as to the extent to which a H+ is in flight in a particular transition state. Neither substrate handling (i.e., on-off steps), nor the isotopic exchange with the solvent, is assumed to be rapid.