A great deal of research on farm and food policy and consumer choice focuses on the link between food consumption and nutrition. This paper presents and applies a new method to analyze the demand for food and nutrients, and consumer welfare. The foundation for this method is the recent extension of the Gorman class of exactly aggregable demand models to incomplete demand systems. The purposes of this approach are to derive and implement coherent, flexible empirical models of food and nutrient demand, to estimate the model parameters consistently with aggregate data, and to make inferences on the impacts of farm and food policy changes on food and nutrient demand and consumer welfare of those policies. We apply this framework to annual per capita U.S. demand for food and nutrients 1919-2000, excluding 1942-1946 to account for World War II. The empirical model is an incomplete system of Gorman Engel curves that is nonlinear in income. This class of demand models generates theoretically consistent, exactly aggregable systems of demand equations for which only a small number of summary statistics for the distribution of income are required to estimate the model's parameters consistently using aggregate data. This model is estimated with 0o homogeneity, monotonicity, symmetry, and a negative semidefinite Slutsky matrix imposed globally, so that the results can be used directly for economic analyses. A complete time series of price and income elasticities of food and nutrient demand are obtained for the sample period.