  We study the performance of gaseous and two-phase (liquid-gas) cryogenic
detectors of ionizing radiation, based on gas electron multipliers (GEMs). For
the first time, high gas gains, exceeding 10^4, were obtained in pure He, Ar
and Kr at low temperatures and the stable avalanche mode of operation was
observed in the two-phase cryogenic detector in Kr. The electron avalanching at
low temperatures, in the range of 120-300 K, is systematically studied.
