As an alternative to the classical assumption o f homogeneous variance model, a normal model whose group error variance is proportional to some unknown power o f the mean has been proposed. When the power takes the value zero it becomes the homogeneous variance model. For the value two, it fits the homogeneous coefficient o f variation model. A maximum likelihood method of solutions is developed. In implementing the method o f scoring, a proper scaling is sought for large simulated ranges o f parameter values. Under some regularity conditions, the solutions are shown to be unique and consistent. In general, the estimates o f the asymptotic variances are smaller than those under the homogeneous variance assumption. The behaviour o f the estimates as the model departs from (a) the homogeneous variance model and (b) the homogeneous coefficient o f variation model are thoroughly studied. An example is shown as an illustration o f the method.