Semiparametric methods have been developed to increase efficiency of inferences in randomized trials by incorporating baseline covariates. Locally efficient estimators of marginal treatment effects, which achieve minimum variance under an assumed model, are available for settings in which outcomes are independent. The value of the pursuit of locally efficient estimators in other settings, such as when outcomes are multivariate, is often debated. We derive and evaluate semiparametric locally efficient estimators of marginal mean treatment effects when outcomes are correlated; such outcomes occur in randomized studies with clustered or repeated-measures responses. The resulting estimating equations modify existing generalized estimating equations (GEE) by identifying the efficient score under a mean model for marginal effects when data contain baseline covariates. Locally efficient estimators are implemented for longitudinal data with continuous outcomes and clustered data with binary outcomes. Methods are illustrated through application to AIDS Clinical Trial Group Study 398, a longitudinal randomized clinical trial that compared the effects of various protease inhibitors in HIV-positive subjects who had experienced antiretroviral therapy failure. In addition, extensive simulation studies characterize settings in which locally efficient estimators result in efficiency gains over suboptimal estimators and assess their feasibility in practice.