We develop a statistical methodology for the assessment of individual bioequivalence when a crossover design is invoked. The location parameters for our model consist of population-averaged parameters for formulation, population-averaged parameters for nuisance effects (sequence, period, carryover, etc.), and subject-specific parameters for formulation. We do not impose any distributional assumptions other than the existence of first- and second-order moments. We derive unbiased estimators for all of the parameters in the model and construct subject-specific bioequivalence scores which exclude the effects of the nuisance parameters. We assess individual bioequivalence by constructing distribution-free tolerance intervals based on the sample of bioequivalence scores.