The paper presents the selected results of consumers’ study of food products in Serbia. It focuses on the products with nutrition and health claims (NHCs) and the analysis of the main consumers’ characteristics which influence their awareness and knowledge about NHCs, their attitudes toward products with NHC and their purchase intentions. Different socio-demographic factors that influence consumers’ behavior were investigated. Education, gender, age and income of the respondents are the key factors which influence awareness, knowledge and consumption. As those products are closely related to consumers’ health, we presented the results based on the differences in health status of the respondents. Main findings show that the respondents with health problems do not consume those products as often as others, which is the outcome of a low level of nutrition knowledge. This represents a major restraining factor for the increase in consumption. After identifying the characteristics of demand, we have suggested some proposals for managers, aimed at overcoming the identified problems, and for government institutions so as to obtain a proactive approach to improving the overall health of the population.