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We report EGRET upper limits on the high-energy gamma-ray emission fromclusters of galaxies. EGRET observations between 1991 and 2000 were analyzed atpositions of 58 individual clusters from a flux-limited sample of nearby X-raybright galaxy clusters. Subsequently, a coadded image from individual galaxyclusters has been analyzed using an adequately adapted diffuse gamma-rayforeground model. The resulting 2 sigma upper limit for the average cluster is\~ 6 x 10^{-9} cm^{-2} s^{-1} for E > 100 MeV. Implications of thenon--detection of prominent individual clusters and of the general inability todetect the X-ray brightest galaxy clusters as a class of gamma-ray emitters arediscussed. We compare our results with model predictions on the high-energygamma-ray emission from galaxy clusters as well as with recent claims of anassociation between unidentified or unresolved gamma-ray sources and Abellclusters of galaxies and find these contradictory.Comment: 13 pages, 6 figures, 2 tables (emulateapj), accepted for publication  in Ap

EGRET Upper Limits on the High‐Energy Gamma‐Ray Emission of Galaxy Clusters