  The diffractive process $\gamma^*(Q^2) p\to V+X$ (where $V= \rho^0, \omega ,
\phi$ are the vector mesons, consisted of light quarks, $X$ represents the
hadrons to that a proton dissociates) is studied. We consider the region of
large momentum transfers, $|t|>>\Lambda^2_{QCD}$, and large energies, s. In the
leading log approximation of perturbative QCD ( using BFKL equation ) the
asymptotic behaviour of the cross section in the limit $s\to\infty , s>>|t|,
Q^2$ is obtained.
  We compare the results derived from BFKL equation with that obtained in the
lowest order of QCD (two--gluon exchange in the $t$- channel). The possibility
to investigate these reactions at HERA is discussed.
