We investigated the dephasing properties of excitons in CdS1-xSex in the compositional range 0.07 less than or similar to x less than or similar to 0.80 by means of transient four-wave-mixing experiments. For 0.35 less than or similar to x less than or similar to 0.80, the dephasing times of localized excitons are in the order of a few 100 ps up to 1 ns. Thereby, we observe a strong dependence of the dephasing times on the composition x, the localization depth and the spectral excitation width. For very short delay times (a few ps), a beat phenomenon is presented which is interpreted by multiple reflections of propagating exciton-polariton wave packets. In the compositional range 0.07 less than or similar to x less than or similar to 0.35 the four-wave-mixing signal is strongly suppressed and the slowly dephasing signal is hardly observable ol as in the most cases not measureable at all.