  The quantum Yang-Mills theory, describing a system of fields with non-dual
(chromo-electric g) and dual (chromo-magnetic \tilde g) charges and revealing
the generalized dual symmetry, is developed by analogy with the Zwanziger
formalism in QED. The renormalization group equations (RGEs) for pure
nonabelian theories are analysed for both constants, \alpha = g^2 / 4\pi and
\tilde\alpha = {\tilde g}^2 / 4\pi. The pure SU(3) \times \widetilde{SU(3)}
gauge theory is investigated as an example. We consider not only monopoles, but
also dyons. The behaviour of the total SU(3) \beta-function is investigated in
the whole region of \alpha \equiv \alpha_s: 0 \le \alpha < \infty. It is shown
that this \beta-function is antisymmetric under the interchange \alpha
\longleftrightarrow 1/\alpha and is given by the well-known perturbative
expansion not only for \alpha \ll 1, but also for \alpha \gg 1. Using an idea
of the Maximal Abelian Projection by t' Hooft, we considered the formation of
strings - the ANO flux tubes - in the Higgs model of scalar monopole (or dyon)
fields. In this model we have constructed the behaviour of the \beta-function
in the vicinity of the point \alpha = 1, where it acquires a zero value.
Considering the phase transition points at \alpha \approx 0.4 and \alpha
\approx 2.5, we give the explanation of the freezing of \alpha_s. The evolution
of \alpha_s^{-1}(\mu) and the behaviour of V_{eff}(\mu) are investigated for
both, perturbative and non-perturbative regions of QCD. It was shown that the
effective potential has a minimum, ensured by the dual sector of QCD. The gluon
condensate F^2_0, corresponding to this minimum, is predicted: F^2_0 \approx
0.15 GeV^4, in agreement with the well-known results.
