  This work presents concisely the results obtained from the analysis of the
two-point function of the gauge field in the $SU(2)$ and $SU(2)\times U(1)$
gauge theories, in the Landau gauge, coupled to a scalar Higgs field in the
fundamental or adjoint representation. Non-perturbative effects are considered
by taking into account the Gribov ambiguity. In general, in both Yang-Mills
models the gluon propagator has non-trivial contributions of physical and
non-physical modes, which clearly depends on the group representation of the
Higgs field. These results were presented during the Fourth Winter Workshop on
Non-perturbative Quantum Field Theory, which took place in Sophia-Antipolis -
France.
