In many econometric studies of demand relationships the design matrix is frequently subject to severe collinearity. In this paper the Generalized Maximum Entropy methodology is introduced and used to estimate a set of demand relationships. The ability of Generalized Maximum Entropy to estimate economic relationships that are typically subject to a high degree of collinearity among the explanatory variables, thus potentially causing traditional methods of estimation to be unreliable, is explained. The results derived by this alternative method of estimation, for a UK meat demand data set, are analysed and examined. The potential for this emerging estimation methodology is discussed.