  This PhD thesis is devoted to show that differential renormalization is a
simple and useful renormalization method that we can use when dealing with
gauge theories. In this work, it is shown how the one-loop results of
Constraint Differential Renormalization can be fruitfully applied when
renormalizing two-loop amplitudes. As an example of this procedure, the
two-loop beta functions of various relevant gauge theories are obtained (QED,
SuperQED, Yang-Mills and N=1 SuperYM) without making use of the Ward
identities, which are mandatory in the standard differential renormalization
procedure. Also, we study how to deal with expressions that have IR and UV
divergences, showing that both are renormalized with independent scales. This
result allow us to give new insight on the origin of the higher order
corrections to the beta function of the N=1 SuperYM theory, as in this case we
have both divergences due to the form of the gauge propagator. This is an
advantage over usual dimensional regularization methods, where both divergences
become mixed.
