In this article, methods are proposed for design and analysis of clinical trials that gather longitudinal data on multiple outcome variables. A valid test of the null hypothesis of no treatment group differences can be obtained for any choice of a working alternative hypothesis and a working covariance matrix for the outcome variables. Increased power can be achieved by accurate modeling of the true treatment effect and covariance structure. Implementation of the procedure is simple using existing software for generalized estimating equations. The procedure is an extension of the 'derived variable' technique (univariate analysis applied to a linear combination of the outcome variables) and also of O'Brien's generalized least squares test. The procedure is extended to allow sequential testing using an arbitrary division of the total type I error rate among repeated hypothesis tests. The methods are illustrated by the design of a study on the safety of dental amalgam fillings, which served as the motivation for the research.