We further study the performance of cryogenic two-phase avalanche detectors, based on Gas Electron Multipliers (GEMs) and operated in an electron-avalanching mode in Kr. Stable operation of the triple-GEM in saturated vapor, above the liquid, has been demonstrated for several hours. The signals induced by 0.5 MeV gamma-rays were recorded from the two-phase detector in coincidences with a BGO counter, aiming at potential applications in Positron Emission Tomography. Charging-up effects were observed at high anode current densities in GEM-based two-phase detectors. (c) 2005 Elsevier B.V. All rights reserved.