We propose an evolutionary scenario for spiral galaxies in rich, compact clusters. Interactions with the environment, probably dominated by the processes in the hot gaseous intergalactic medium, remove the gas from the disks of blue objects infalling into cluster cores from outer layers. Predictions are made for UBV colors of cluster spirals versus the redshift z, accounting for cosmological and evolutionary effects, by means of a model of spectrophotometric evolution. We show that spirals stripped at ages corresponding to z≃0.5 very rapidly acquire redder colors and an earlier appearance. The fraction of blue objects in compact and open clusters, observed by Butcher and Oemler, may possibly be interpretated.