  The irradiation of atoms by a strong IR laser field of frequency $\omega$
results in the emission of odd-harmonics of $\omega$ ("IR harmonics") up to
some maximal cut-off frequency. The addition of an XUV field of frequency
$\tilde{q}\omega$ larger than the IR cut-off frequency to the IR driver field
leads to the appearance of new higher-order harmonics ("XUV harmonics")
$\tilde{q} \pm 2K, 2\tilde{q} \pm (2K-1), 3\tilde{q} \pm 2K,...$ ($K$ integer)
which were absent in the spectra in the presence of the IR field alone. The
mechanism responsible for the appearance of the XUV harmonics is analyzed
analytically using a generalization of the semiclassical re-collision
(three-step) model of high harmonic generation. It is shown that the emitted
HHG radiation field can be written as a serie of terms, with the HHG field
obtained from the three-step model in its most familiar context [P. B. Corkum,
\textit{Phys. Rev. Lett.} {\bf 71}, 1994 (1993)] resulting from the
zeroth-order term. The origin of the higher-order terms is shown to be the
ac-Stark oscillations of the remaining ground electronic state which are
induced by the XUV field. These terms are responsible for the appearance of the
new XUV harmonics in the HGS. The XUV harmonics are formed by the same electron
trajectories which form the IR harmonics and have the same emission times, but
a much lower intensity than the IR harmonics, due to the small quiver amplitude
of the ac-Stark oscillation. Nevertheless, this mechanism allows the extension
of the cut-off in the HGS without the necessity of increasing the IR field
intensity, as is verified by numerical time-dependent Schr\"{o}dinger equation
simulation of a Xe atom shined by a combination of IR and XUV field.
