The optical properties of CdSe nanostructures grown by migration-enhanced epitaxy of CdSe on ZnSe are studied by time-, energy-, and temperature-dependent photoluminescence and excitation spectroscopy, as well as by polarization-dependent four-wave mixing and two-photon absorption experiments. The nanostructures consist of a coherently strained Zn 1Ϫx Cd x Se/ZnSe quantum well with embedded islands of higher Cd content with sizes of a few nanometer due to strain-induced CdSe accumulation. The local increase in CdSe concentration results in a strong localization of the excitonic wave function, in an increase in radiative lifetime, and a decrease of the dephasing rate. Local LO-phonon modes caused by the strong modulation of the Cd concentration profile are found in phonon-assisted relaxation processes. Confined biexcitons with large binding energies between 20 and 24 meV are observed, indicating the important role of biexcitons even at room temperature. ͓S0163-1829͑99͒16935-2͔