  We predict the dependence on energy of photo(electro) production processes:
$\gamma(\gamma^*)+p\to V+ X$ with large rapidity gap at small x and large
momentum $-t$ transferred to $V$ in pQCD. Here V is a heavy quarkonium
($J/\psi, \Upsilon$) or longitudinally polarized light vector meson (in the
electroproduction processes), etc. In the kinematics of HERA we calculate the
dependence on energy of cross sections of these processes as the function of
momentum transfer $t$, photon virtuality $Q^2$ and/or quarkonium mass. In the
kinematical region $Q_0^2\le -t\ll Q^2+M^2_V$ the nontrivial energy dependence
of the cross section for the vector meson production due to the photon
scattering off a parton follows within QCD from the summing of the double
logarithmic terms. In the second regime $-t\ge Q^2+M^2_V$ within DGLAP
approximation in all orders of perturbation theory the $q\bar q - {\rm parton}$
elastic cross section is energy independent. We show that the correct account
of the double logarithmic terms and of the gluon radiation including
kinematical constraints removes the disagreement between pQCD calculations and
recent HERA experimental data. The explicit formula for the dependence of the
differential cross section$\displaystyle{\frac{d^2\sigma}{dtdx_J}}$ of these
processes on $s_{\gamma^*N}$ is obtained. We show that perturbative Pomeron
type behavior may reveal itself only at energies significantly larger than
those available at HERA. In addition we evaluate the energy dependence of DCVS
processes.
