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We present a general mathematical procedure to handle interactions described by a Morse potential in the presence of a strong harmonic excitation. We account for permanent and field-induced terms and their gradients in the dipole moment function, and we derive analytic formulae for the bond-length change and for the shifted energy eigenvalues of the vibrations, by using the Kramers–Henneberger frame. We apply these results to the important cases of H _2 and LiH, driven by a near- or mid-infrared laser in the 10 ^13  W cm ^−2 intensity range.