Luminescence spectra of poly-N-epoxypropylecarbazole (PEPC), poly-N-epoxypropyle-3,6- dichlorocarbazole (DClPEPC), and poly-N-epoxypropyle-3,6-dibromocarbazole (DBrPEPC) films, both pure and with the bis[2-(2′ -benzothienyl)-pyridinato-N,C3′ ](acetylacetonate) iridium (Btp2Ir(acac)) admixture, polystyrene (PS) films with the Btp2Ir(acac) admixture, and composite films of PEPC with the benzophenone and Btp2Ir(acac) admixtures have been studied. Those polymers are promising for their application in optoelectronic devices. It is found that, in the case of PEPC matrix, the excitation energy is transferred both via singlet excitons (through migration and long-range dipole-dipole interaction) and triplet ones (due to the migration and short-range electron exchange interaction). At the same time, in the films based on phosphorescent DBrPEPC, the energy transfer is only provided by triplet excitons. It is found that the quantum yield of the sensitized phosphorescence for Btp2Ir(acac) molecules in the carbazolyl-containing polymer matrix is lower than that under their direct excitation in the PS matrix. For the PEPC-based composite, this parameter is found to be three and five times higher than that for the DClPEPC and DBrPEPC matrices, respectively. The additional doping of the PEPC-based composite with benzophenone gave rise to the transformation of some singlet excitons into triplet ones and, as a result, to a reduction of the sensitized Btp2Ir(acac) phosphorescence intensity. A conclusion is drawn that, during the migration, some of both singlet and triplet excitons became localized in the tail energy states, and a certain fraction of triplet excitons is trapped by polymer oxidation products.