Cell competition is a homeostatic process that eliminates by apoptosis unfit or undesirable cells from animal tissues, including tumor cells that appear during the life of the organism. In Drosophila there is evidence that many types of oncogenic cells are eliminated by cell competition. One exception is cells mutant for polyhomeotic (ph), a member of the Polycomb family of genes; most of the isolated mutant ph clones survive and develop tumorous overgrowths in imaginal discs. To characterize the tumorigenic effect of the lack of ph, we first studied the growth of different regions of the wing disc deficient in ph activity and found that the effect is restricted to the proximal appendage. Moreover, we found that ph-deficient tissue is partially refractory to apoptosis. Second, we analyzed the behavior of clones lacking ph function and found that many suffer cell competition but are not completely eliminated. Unexpectedly, we found that nonmutant cells also undergo cell competition when surrounded by ph-deficient cells, indicating that within the same tissue cell competition may operate in opposite directions. We suggest two reasons for the incompleteness of cell competition in ph mutant cells: 1) These cells are partially refractory to apoptosis, and 2) the loss of ph function alters the identity of imaginal cells and subsequently their cell affinities. It compromises the winner/loser interaction, a prerequisite for cell competition.