  We study the reactions $\gamma^*(Q^2)p\to\rho^0 p$ and
$\gamma^*(Q^2)p\to\gamma^*(Q^2) p$ at large Q^2 and $W^2/Q^2$ and small
momentum transfer, $\kappa^2_\perp$, to the nucleon where the pomeron exchange
dominates. At large Q^2 the virtual photon selects a hard $q\bar q$ pair, thus
selecting the hard pomeron component (the BFKL pomeron). The amplitudes for
both transverse and longitudinal polarizations of the initial photon and
outgoing $\rho$-meson (photon) are calculated in the framework of the BFKL
pomeron exchange. Our calculations show that one cannot expect the early onset
of the pure perturbative regime in the discussed diffractive processes: the
small interquark distances, $\rho_{q\bar q} <0.2$ fm, start to dominate not
earlier than at $Q^2 \simeq 100 GeV^2, W^2/Q^2 \simeq 10^7$ in
$\gamma^*(Q^2)p\to\rho^0 p$ and $Q^2 \simeq 50 GeV^2, W^2/Q^2 \simeq 10^6$ in
$\gamma^*(Q^2)p\to\gamma^*(Q^2) p$.
