  We study the ultraviolet properties of theories whose fundamental fields
display a confining, Gribov-type, propagator. These are propagators that
exhibit complex poles and violate positivity, thus precluding a physical
propagating particle interpretation. We show that the properties of this type
of confining propagators do not change the ultraviolet behavior of the theory,
in the sense that no new ultraviolet primitive divergences are generated, thus
securing the renormalizability of these confining theories. We illustrate these
properties by studying a variety of models, including bosonic and fermionic
confined degrees of freedom. The more intricate case of Super Yang-Mills with
${\cal N} =1$ supersymmetries in the Wess-Zumino gauge is taken as example in
order to prove these statements to all orders by means of the algebraic
renormalization set up.
