  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
$\mathrm{H}_{2}$ and $\mathrm{LiH}$, driven by a near- or mid-infrared laser in
the $10^{13}$ $\mathrm{ W/cm^2}$ intensity range.
