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Two I o x I o fields of the Pleiades region, containing 78 cluster members within a limiting magnitude of 14 mag and centered on two of the most luminous stars of the cluster (20 Tau and 17 Tau) have been observed with the Einstein (HEAO 2) Observatory imaging proportional counter. The exposure times (~3-4 x 10 3 s) and background level give, at the Pleiades distance (~127 pc), a mean detection threshold of 10 29 5 ergs s-1. We have detected one (out of eight) B stars, one (out of 13) A stars, two (out of 10) F stars, 11 (out of 21) G stars and six (out of more than 26) K stars. The brightest X-ray source is Hz II 253 (Gl), with L x « io 30-3 ergs s" 1. We derive the maximum-likelihood X-ray luminosity functions for the G and K stars in the cluster, and show that for the G stars, the Pleiades X-ray luminosity function is significantly brighter than the corresponding function for Hyades G dwarf stars. The significantly larger number of X-ray bright G stars than K stars (even though the Pleiades K stars appear to be relatively rapid rotators), and the lack of detection of M stars, suggest that the connection between stellar rotation and the level of X-ray emission is not as straightforward as has been heretofore thought.