The X-ray source in Perseus identified as NGC 1275 is found to have a finite angular extent of about 33 arc minutes. The improved location of the center of the emission is consistent with NGC 1275. An improved location for the center of the Coma X-I source is consistent both with the kinematic center of the cluster and with NGC 4874. The Perseus X-ray spectrum fits a powerlaw index of 1.09 + 0.07; the Coma spectrum fits either a power law of index 1.01 1 0.10 or a thermal-bremsstrahlung spectrum with kT = 5.3 1 0.6 keV. These extended sources-Coma, Perseus, and the source in the Virgo cluster-may be a new class of X-ray objects associated with active galaxies in rich clusters.