Number of Tunisian food demand studies have measured the influence of traditional variables, such as income and prices, and in some cases some socio-demographic variables. However, given increasing concerns about health, other important factors, such as the nutritious quality and the nutrient content of food, have also been shown to determine consumer choices. This paper analyses the effect of these factors on the demand for dairy products. The nutritious quality of dairy products is measured by an index that relates nutrient content of each product with the standards suggested by the National Academy of Science. A demand system is estimated and nutrient demand elasticities with respect to prices and expenditure are obtained. Results differ from traditional studies in the sense that higher prices do not indicate lower consumption but a shift to a higher quality demand.