Measurements were carried out which related to two different ages of the prehistory of Hungary which had not been previously dated directly by radiocarbon. Bone samples were taken from graves which belong to the Middle Copper Age (Bodrogkeresztur culture) and to the Late Iron Age (early La Tène). The treatment of bone samples is discussed. A quadrupole mass spectrometer was used to check the absence of nitrogen oxides after purification of carbon dioxide. Most of the measured conventional radiocarbon dates of the bone samples are in good agreement with the previously determined chronologies.