Two models for the third-order response function of a two-electronic level chromophore are investigated. The first assumes an excited state vibrational Hamiltonian whose phonon modes exhibit both linear and diagonal quadratic electron-phonon coupling. Impulsive stimulated photon echoes are calculated for this model. The second assumes linear electron-phonon coupling including vibrational relaxation and pure electronic dephasing. Impulsive two-pulse photon echo signals and their dependence on temperature and electron-phonon coupling strength are calculated for this model. The initial fast nonexponential (free-induction) decay due to all multiphonon transitions, quantum beats and the slow decay component due to the zero-phonon line (pure electronic dephasing) are identified and correlated with features of the single-site absorption spectrum whose relationship to the hole burned spectrum is well understood. Pure electronic dephasing associated with the zero-phonon line contributes to the decay of the quantum beats. This contribution may be non-negligible at high temperatures in certain systems. An application is made to the special pair absorption band of the bacterial reaction center.