The first gamma spectra associated with the annihilation of positrons with individual core levels (Cu 3p and Ag 4p) are presented. The spectra were obtained by measuring the energy of gamma rays time coincident with Auger electrons emitted as a result of positrons annihilating with a selected core level. Relativistic calculations show good agreement with experiment over a limited range of momenta. However, statistically significant differences indicate that the measurements can provide an impetus to new calculations of many body effects in positron-core electrons annihilation.