Photoluminescence and photoluminescence excitation spectra, vertical transport of photoexcited charge carriers and excitons and Raman scattering by optical phonons have been studied for the first time in low-strained superlattices CdSe/CdMgSe grown by molecular-beam epitaxy on InAs substrates. The vertical transport was studied by purely optical means involving an enlarged quantum well built into the superlattice. The enlarged quantum well served as a sink for the photoexcited carriers and excitons that have tunnelled through the superlattice. The measurements conducted in temperature range 2–150 K and also under in-plane strong magnetic fields show that vertical transport occurs mainly by free heavy-hole excitons but in superlattices with 5.9 nm and 7.3 nm periods it is not of the Bloch type. A comparison of the calculated energies of the interband transitions with the experimental data provides the valence-band ofsett in the range 0.4–0.5. The Raman spectra indicate a two-mode behavior of the optical phonons in CdMgSe barriers. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)