  In this paper we consider the presence of the Wu-Yang magnetic monopole in
the global monopole spacetime and their influence on the vacuum polarization
effects around these two monopoles placed together. According to Wu-Yang [Nucl.
Phys. {\bf B107}, 365 (1976)] the solution of the Klein-Gordon equation in such
an external field will not be an ordinary function but, instead, {\it section}.
Because of the peculiar radial symmetry of the global monopole spacetime, it is
possible to cover its space section by two overlapping regions, needed to
define the singularity free vector potential, and to study the quantum effects
due to a charged scalar field in this system. In order to develop this analysis
we construct the explicit Euclidean scalar Green {\it section} associated with
a charged massless field in a global monopole spacetime in the presence of the
Abelian Wu-Yang magnetic monopole. Having this Green section it is possible to
study the vacuum polarization effects. We explicitly calculate the renormalized
vacuum expectation value $<\Phi(x)^*\Phi(x) >_{Ren.}$, associated with a
charged scalar field operator and the respective energy-momentum tensor,
  $<T_{\mu\nu}(x)>_{Ren.}$, which are expressed in terms of the parameter which
codify the presence of the global and magnetic monopoles.
