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.