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In the Sumi model describing the effect of the exciton—phonon coupling on excitons in molecular crystals by a stochastic Markoff‐Gauss process with a site‐diagonal potential with a time‐dependent exponentially decaying correlation function, the phononless exciton lineshape is investigated. It is proved that in general, cumulants of all even orders contribute to the optical lineshape function due to non‐commutativity of relevant operators at different times. So the recent result by Blumen and Silbey is shown to be just an approximation neglecting all but second‐order cumulants. The fourth‐order correction is calculated and it is proved that starting from this order of approximation, the free‐exciton density of states does not give a sufficient information necessary to deduce the optical lineshape function.