  We consider two coupled problems.
  We study the dependence on photon virtuality $Q^2$ for the semihard
quasi--elastic photoproduction of neutral vector mesons on a quark, gluon or
real photon (at $s\gg p_{\bot}^2,\;Q^2; \; p_{\bot}^2\gg \mu^2 \approx (0.3$
GeV)$^2$). To this end we calculate the corresponding amplitudes (in an
analytical form) in the lowest nontrivial approximation of perturbative QCD. It
is shown that the amplitude for the production of light meson varies very
rapidly with the photon virtuality near $Q^2=0$.
  We estimate the bound of the pQCD validity region for such processes. For the
real incident photon the obtained bound for the $\rho$ meson production is very
high. This bound decreases fast with the increase of $Q^2$, and we expect that
the virtual photoproduction at HERA gives opportunity to test the pQCD results.
The signature of this region is discussed. For the hard Compton effect the pQCD
should work good at not too high $p_{\bot}$, and this effect seems measurable
at HERA.
