The Growth Curve model (POTTHOFF ROY 1964) is studied. We obtain moments of order up to 6 for the maximum likelihood estimator of B in E [X] = ABC and the first and second ordr moments of the maximum likelihood estimator of the dispersion matrix are obtained. In order to apply the moment expressions the moments are in turn estimated. all results of the paper are based on moments for matrix normally, WISHART and inverted WISHART distributed variables. An extended model, allowing for covariates, is alos treated