Two loop divergences studied with one loop constrained differential renormalization

In the context of differential renormalization, using constrained differential renormalization rules at one-loop, we show how to obtain concrete results in two-loop calculations without making use of Ward identities. In order to do that, we obtain a list of integrals with overlapping divergences compatible with CDR that can be applied to various two-loop background field calculations. As an example, we obtain the two-loop coefficient of the beta function of QED, SuperQED and Yang-Mills theory.