A local SU(2) gauge theory with one multiplet of scalars in the adjoint representation is considered. In the limit of infinite gauge coupling constant ($g=\infty$), Yang-Mills fields become auxiliary and the action possesses a larger invariance than the usual gauge invariance; hence, the system develops a richer structure of constraints. The constraint analysis is carried out, the Faddeev-Popov-Senjanović determinant is evaluated, and all the functional integrals in the generating functional $W\left[J\right]\mathrm{}$ over all canonical momenta, as well as over the gauge fields $A_{\mu }^a$ and two of three components of the scalar field ${\phi }_a$, are evaluated, yielding the extremely curious result that, in this limit ($g=\infty$), the original theory is equivalent to a one-component self-interacting real scalar theory. This is an exact nonperturbative result. Some possible implications of this result are discussed.

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