Although the physical background for this algeba was indicated in part one, last week, this talk will deal with the purely mathematical aspects of the Hopf algebra map from the Connes-Moscovici Hopf algebra to the Hopf algebra of Feynemnan diagrams. Both Hopf algebras will be recalled. IF this takes only half the hour, Jim Stasheff will continue with his report from the ESI: Pre-Lie algebras are alive and well...