Attempts to estimate demand equations can, roughly, be classified into two groups. To the first group belong those studies which concentrate on an empirically acceptable explanation of demand for individual commodities, while the overall relationships between the quantities demanded of all commodities in the budget remain in the background. The second group of studies is chiefly concerned with the allocation aspect of consumer demand and has complete systems of demand equations as its object. The overall restrictions on demand equations provided by the theory of consumers' choice play a dominant role in these studies. The following article belongs to the second group. It considers a complete system of demand equations with coefficients which satisfy the theoretical restrictions in an exact way. The estimation of these coefficients is complicated by the nonlinear nature of the restrictions and the interdependence between the equations. These difficulties are not insurmountable as will be clear from the article itself.