The nuclear Schwinger-Dyson formalism incorporating sigma and omega me
sons is generalized to treat asymmetric nuclear matter and to investig
ate the effects of higher order diagrams, in particular ring diagrams.
The new point of the generalization is to treat separately the contri
butions from protons and those from neutrons to self-energies. It is s
hown that the ring diagrams work attractively in a wide region of the
baryon density and asymmetry, and that the ring diagrams are very impo
rtant in reducing the asymmetry energy from the value of Hartree Fock
(HF).