Stability of galaxy clusters: neutral hydrogen observations

New upper limits are obtained for the 21-cm emission from the Cancer, Coma, Pegasus I, and Perseus clusters of galaxies. In all cases these limits correspond to a galactic mass (1011 M0) of optically thin neutral hydrogen. These observations rule out the possibility that the Coma cluster is gravitationally bound by rotationally supported, optically thick clouds of neutral hydrogen. The conclusion concerning the remaining clusters is less certain, and more optical and radio data are needed. Subject headings: galaxies, clusters of - intergalactic medium - 21-cm radiation