  The ultraviolet asymptotic behavior of the gluon propagator is evaluated in
the maximal Abelian gauge in the SU(2) gauge theory on the basis of the
renormalization-group improved perturbation theory at the one-loop level.
Square-root singularities obtained in the Euclidean domain are attributed to
artifacts of the one-loop approximation in the maximal Abelian gauge and the
standard normalization condition for the propagator used in our study. It is
argued that this gauge is essentially nonperturbative.
