Several features of the production of Na/sup 24/ and Mg/sup 28/ fragments produced in the interaction of protons and He ions with Cu, Ag, Au, and U were investigated. Formation cross sections were determined for He ions of different energies between 320 and 880 Mev and for protons of 700 Mev. Thick- target recoil experiments were performed at bombarding energies of 0.7 and 3 Bev for protons, and 880 Mev for He ions. Also given are some recoil measurements of Na/sup 24/ from Al. Analysis of data obtained with target materials heavier than Al showed that for the bombarding energies used, Na/sup 24/ and Mg/sup 28/ are probably produced by the cleavage of the target nucleus into two heavy fragmerts. One of these fragments has a mass approximately equal to the mass Na 4 or Mg/6 and the other contains most of the remaining mass of the target nucleus. However, Na/sup 24/ and Mg/sup 28/ are very probably not slowly evaporated particles nor products of a slow fission process. The experimental information covering fragmentation from photographic emulsion studies and radiochemical studies is discussed. The various mechanisms proposed are considered and a new one suggested. According to this new mechanism Na/sup …