  The general method for calculation of valence quark distributions in hadrons
at intermediate $x$ is presented. The imaginary part of virtual photon forward
scattering amplitude on quark current with hadron quantum number is considered
in the case, when initial and final virtualities of the current $p^2_1$ and
$p^2_2$ are different, negative and large: $\mid p^2_1\mid, \mid p^2_2\mid\gg
R^{-2}_c$, where $R_c$ is confinement radius. The operator product expansion
(OPE) in $p^2_1,p^2_2$ up to dimension 6 operators is performed. Double
dispersion representations in $p^2_1, p^2_2$ of the amplitude in terms of
physical states contributions are used. Equalling them to those calculated in
QCD by OPE the desired sum rules for quark distributions in mesons are found.
The double Borel transformations are applied to the sum rules, killing
non-diagonal transition terms, which deteriorated the accuracy in the previous
calculations of quark distributions in nucleon. Leading order perturbative
corrections are accounted. Valence quark distributions in pion, longitudinally
and transversally polarized $\rho$-mesons and proton are calculated at
intermediate $x$, $0.2 \la x \la 0.7$ and normalization points $Q^2 = 2-5
\~GeV^2$ with no fitting parameters. In cases of pion and proton the results
are in agreement with found correspondingly from the data on the Drell-Yan
process and deep inelastic scattering. Valence quark distributions in
transversally and longitudinally polarized $\rho$-mesons are essentially
different one from another and also differ from those in pion.

High Energy Physics - Phenomenology