Effective action for non-Abelian fields with non-vanishing sources

Interaction with external source results in the appearance of secondary relation instead of gauge condition. On the basis of the note the amplitude of vacuum-vacuum Z(J) and effective action G(A) are determined by the method free of gauge ambiguity. It is sown, that functional Z(J) is covariant, and G(A) is invariant during gauge transformations of their respective arguments. They can serve as generating functionals. The approach formulated permits not to use the method of background field in cases, when the source does not equal zero. Effective action is calculated in one-loop approximation for pure SU(2) Yang-Mills theory with a special non-Abelian C-numerical, static and homogeneous field, generated by a finite source