Bioequivalence and clinical equivalence trials evaluate the similarity of two or more treatments. For continuous responses, equivalence is demonstrated if a 90% confidence interval for the ratio of treatment means is contained within a prespecified limit, usually 0.8-1.25. When multiple response criteria are evaluated, investigators might conclude overall treatment equivalence if equivalence is demonstrated for each outcome. The power to detect equivalence for all outcomes decreases as the number of outcomes increases, and is affected by correlation between responses. Power of the multiple 90% confidence interval method is evaluated for bivariate log-normal data from parallel and cross-over designs using numerical integration and simulation. Correlation is found to have a stronger effect on multivariate power when each univariate power is moderate to low. Equivalence for dichotomous responses is evaluated with one-sided confidence intervals for odds ratios, ratios, and differences of proportions. Univariate and bivariate power are evaluated for each definition. Confidence intervals for differences appear to have the best power for response proportions near 1.0, but power for differences and odds ratios is similar for response proportions near 0.5. Equivalence can alternately be defined in terms of the ratio of an individual's response to two treatments. A method of evaluating individual equivalence is presented ,based on ANOVA prediction intervals for an individual's ratio of responses from cross-over designs with log-normal data. Univariate and bivariate power are evaluated for this method.