A model, in which the means and the variance-covariance matrix of observed variables change with an external variable, is proposed. This is an extension of the analysis of covariance structures in several populations. Assuming that the observed variables, given the value of an external variable, have a multivariate normal distribution, the maximum likelihood estimates of the parameters in the model can be obtained by the Fisher's scoring method. The model with a constant variance-covariance matrix, the model with constant correlations, the model of a single common factor and the model of oblique multiple factors with constant factor loadings are disucussed for the model of the variance-covariance matrix. Finally, examples of intelligence test scores are provided, where the external variable is age.