Performance of GEM detectors in high intensity particle beams

We describe extensive tests of Double GEM and Triple GEM detectors, including full size prototypes for the COMPASS experiment, exposed to high intensity muon, proton and pion beams at the Paul~Scherrer Institute and at CERN. The measurements aim at detecting problems possible under these operation conditions, the main concern being the occurrence of discharges induced by beam particles. Results on the dependence of the probability for induced discharges on the experimental environment are presented and discussed. Implications for the application of GEM~detectors in experiments at high luminosity colliders are illustrated.