  We extend the method of differential renormalization to massive quantum field
theories treating in particular $\ph4$-theory and QED. As in the massless case,
the method proves to be simple and powerful, and we are able to find, in
particular, compact explicit coordinate space expressions for the finite parts
of two notably complicated diagrams, namely, the 2-loop 2-point function in
$\ph4$ and the 1-loop vertex in QED.
