  We discuss a few, apparently different (but actually, tightly related)
problems: 1. The relation between QCD and valence quark model, 2. The
asymptotic behavior of the nonperturbative pion wave function $\psi(\k, x)$ at
$x\rightarrow 0,~1, \k \rightarrow \infty$ and 3. The dimensional counting
rules in the intermediate region of energy. The analysis is based on such
general methods as dispersion relations, duality and PCAC. We calculate the
asymptotic behavior of the wave function ($wf$) at the end-point region
($x\rightarrow 1$ and $\k\rightarrow\infty$) by analysing the corresponding
large $n-$th moments in transverse $\la\vec{k}_{\perp}^{2n}\ra \sim n!$ and
longitudinal $\la (2x-1)^n\ra \sim 1/n^2$ directions. This information fixes
the asymptotic behavior of $wf$ at large $\k$ ( which is turned out to be
Gaussian commonly used in the phenomenological analyses). We discuss some
applications of the obtained results. In particular, we calculate the
nonleading ``soft" contribution to the pion form factor at intermediate
momentum transfer. We argue, that due to the specific properties of $\psi(\k,
x)$, the corresponding contribution can temporarily {\bf simulate} the leading
twist behavior in the extent region of $ Q^2 $. The same effect also takes
place for the nucleon formfactor. Such a mechanism, if it is correct, would be
an explanation of the phenomenological success of the dimensional counting
rules at available, very modest energies for many different processes. We
discuss some inclusive amplitudes also.
