The low-temperature photoluminescence (PL) and PL excitation (PLE) spectra of two systems of CdTe quantum wells (QWs) separated by CdMnTe and CdMgTe barriers 20 nm thick are studied. The experimental PL spectra are compared with calculations that take into account the exciton effect and the influence of internal strains. The scatter of our data does not exceed that expected for monolayer fluctuations of the QW width. In the PLE spectra of a thick QW, bands were found that correspond to the increase of PL from a thick QW upon excitation of a neighbor narrow QW. The mechanism of energy transfer between QWs separated by thick barriers is discussed. Keywords: CdTe, quantum wells, photoluminescence, photoluminescence excitation.