The use of random-effects models for the analysis of longitudinal data with missing responses has been discussed by several authors. This article extends the random-effects model for a single characteristic to the case of multiple characteristics, allowing for arbitrary patterns of observed data. Two different structures for the covariance matrix of measurement error are considered: uncorrelated error between responses and correlation of error terms at the same measurement times. Parameters for this model are estimated via the EM algorithm. The set of equations for this estimation procedure is derived; these equations are appropriately modified to deal with missing data. The methodology is illustrated with an example from clinical trials.