In recent times, a large number of radiocarbon dates appeared for the Southern Neolithic on the basis of pottery dating because other organic matter has practically not been preserved. There are two organic fractions of pottery useful for dating: food residues and carbon from the pottery matrix itself. Food residues are often dated, but this material is not always preserved and is prone to being removed during the cleaning of the pottery. The clay mass of the pottery contains carbon, often directly visible upon breaking of the pottery. The article focusses on determining the chemical composition of the organic fractions in the pottery and the origin of the carbon. For this aim we used the nuclear magnetic resonance (NMR) method to identify the chemical compounds in the food residue and in the pottery matrix. As an example we used pottery from the Neolithic sites: Zamost’e (Central Russia) and the Varfolomeevskay sites (Southern European Russia, Low Volga region) from archaeological collections. The results obtained demonstrate that the food residue and the pottery matrix contain practically the same organic compounds, even if the relative abundances of various compounds are different in these materials. The origin of the carbon from pottery is discussed.