The dephasing of excitons in self-organized CdSe/ZnSe islands grown by molecular-beam epitaxy is investigated using spectrally resolved four-wave mixing. A distribution of dephasing times is observed, indicating the existence of localized excitons with different relaxation times at comparable transition energies. Polarization-dependent measurements identify the formation of biexcitons. The observed large biexciton binding energy of 22 meV increases with decreasing exciton energy, which is attributed to an increasing three-dimensional confinement.