  We present a generic approach for treating the effect of nuclear motion in
the high-order harmonic generation from polyatomic molecules. Our procedure
relies on a separation of nuclear and electron dynamics where we account for
the electronic part using the Lewenstein model and nuclear motion enters as a
nuclear correlation function. We express the nuclear correlation function in
terms of Franck-Condon factors which allows us to decompose nuclear motion into
modes and identify the modes that are dominant in the high-order harmonic
generation process. We show results for the isotopes CH$_4$ and CD$_4$ and
thereby provide direct theoretical support for a recent experiment [Baker {\it
et al.}, Science {\bf 312}, 424 (2006)] that uses high-order harmonic
generation to probe the ultra-fast structural nuclear rearrangement of ionized
methane.
