We have studied the operation of the Gas Electron Multiplier (GEM) in gas mixtures Xe-CO2, Ar-CO2 and CH4 at different pressures varying from 0.1 to 5 atm. In Ar- and Xe-based mixtures, the maximum GEM gain considerably decreases with pressure, from a few hundreds at 1 atm to below 10 at 5 atm. Combined gain of GEM and the Micro-Strip Gas Chamber (MSGC) can exceed values of 10000 at 1 atm and 100 at 5 atm. High GEM gains, of above 1000, were obtained in CH4 at low pressures. We have observed the effect of the avalanche confinement in GEM micro-holes, resulting in violation of the pressure scaling and in the possibility of GEM operation in pure noble gases. (C) 1998 Elsevier Science B.V. All rights reserved.