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The nonperturbative quantization technique \`{a} la Heisenberg is applied fornon-Abelian gauge theories. The operator Yang-Mills equation is written, whichon the corresponding averaging gives an infinite set of equations for all Greenfunctions. We split all degrees of freedom into two groups: in the former, wehave $A^a_\mu \in \mathcal G \subset SU(N)$, and in the second group we havecoset degrees of freedom $SU(N) / \mathcal G$. Using such splitting and someassumptions about 2- and 4-point Green functions, we truncate the infinite setof equations to two equations. The first equation is for the gauge fields fromthe subgroup $\mathcal G$, and the second equation is for a gluon condensatewhich is the dispersion of quantum fluctuations of the coset fields. Twoexamples are considered: The first one is a flux tube solution describinglongitudinal color electric fields stretched between quark and antiquarklocated at the $\pm$ infinities. The second one is a flux tube stretchedbetween two quarks (antiquarks) located at $\pm \infty$. A special case isconsidered when the longitudinal electric field produced by a quark located at$+ \infty$ is equal and oppositely directed to the field generated by a quarklocated at $- \infty$ that leads to zero total electric field. Both solutionsrepresents the dual Meissner effect: the electric field is pushed out from thegluon condensate.

Nonperturbative quantization \`a la Heisenberg for non-Abelian gauge theories: two-equation approximation