Multivariate observations obtained from chemical and biological experiments often relate several responses to a common set of parameters. In several fields of application, the response functions can be put in the form of a general multivariate linear model, which originates from the analysis of growth curves. System overdetermination is frequently encountered with this model because the number of variables that can be directly measured is larger than the number needed for full identification of the system. These measured variables usually satisfy certain equality constraints, which may come from material balances, for example. The covariate adjustment technique is particularly useful in the analysis of multiresponse models when the responses are related by equality constraints and the covariates are associated with these constraints. Methods to select covariates and criteria to evaluate the results are presented and applied to a set of experimental data. The technique yields maximum likelihood estimates of the desired parameters. The results show that the methods presented yield good parameter estimates.