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The excitonic and vibronic spectra of a molecular chain and of a crystal of NNЈ-dimetyl 3,4,9,10-perylene tetracarboxylic diimide ͑MePTCDI͒ are studied in the case when: ͑i͒ a Frenkel exciton ͑FE͒ and charge transfer excitons ͑CTEs͒ mix strongly; and ͑ii͒ two mechanisms of coupling between these mixed excitons and intramolecular vibrations, notably linear and quadratic coupling, are acting. Using a convenient canonical transformation and the Green function method, we calculate the linear optical susceptibility: ͑a͒ in the exciton region taking into account the contribution of the transition dipoles of FE; and ͑b͒ in one-phonon vibronic regime. The spectra of linear absorption in the excitonic and vibronic regions have been calculated introducing the exciton parameters of MePTCDI. These spectra exhibit: ͑i͒ a relative separation of vibronics of FE and CTEs; ͑ii͒ a stronger impact of the linear coupling on the intensity of the excitonic and vibronic spectra; and ͑iii͒ the appearance of a spectral doublet of vibronics of the CTEs-its splitting depends on the parameters of linear and quadratic exciton-phonon coupling in the neutral excited molecule and ions. Moreover, in the case of weak linear exciton-phonon coupling the vibronic line of FE, being wide and flat, lies in many-particle continuum while in the case of intermediate and strong linear coupling the linear absorption is dominated by the bound exciton-phonon states and their narrow Lorentzian maxima depend strongly on the quadratic coupling.

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