A neutron star in a binary star system can also accrete matter from the companion star on its surface. Combined hydrogen and helium burning ignites when the accreted layer of degenerate matter reaches a density of 10 – 10 g/cm and a temperature exceeding 0.2 GK. This leads to thermonuclear burning comparable to what happens in the outwards moving shockfront of subChandrasekhar supernovae. The neutron star itself is not affected by the explosion and therefore the nuclear reactions in the accreted layer can proceed longer than in an explosion. This allows to establish an rp-process. It will continue until either all free protons are used up or the burning layer has expanded due to the increase in temperature and its density falls below the one required for the nuclear reactions.