The dynamical Stark effect of excitons in CdS bulk crystals has been measured recently using differential transmission spectroscopy (DTS). A general DTS formula is derived taking into account exciton-exciton interaction. A perculiar influence of the pump and test polarization on its magnitude is predicted. Concerning the dephasing (transverse relaxation), coupling to optical phonons is treated on a microscopic level. A density-matrix approach leads to the imaginary part of the exciton-phonon self energy. Its strong frequency dependence which shows up as a non-Markoff relaxation strongly suppresses the relaxation for the pump pulse at large detuning. A more sophisticated approach using the non-equilibrium Green function gives deeper insight into the underlying scattering processes.