This paper is a continuation of a previous paper which has recently appeared in this journal, on the implications of group theory for the foundations of Quaternionic Quantum Mechanics. It is first proved that even in this case a relativistic description is possible. It is then shown that the elementary systems for the Poincaré group, as they appear in this realization, are in one-to-one correspondance with those of the usual complex quantum mechanics. The occurence of charge conjugation related to space reflexion is discussed and some consequences on a TCP-relativistic theory are explored. The framework of a general relativistic Quaternionic Quantum Mechanics is then developped and the particular ties that exist between this theory and its complex analog are emphasized. The possible adequacy of a mixed complex-quaternionic description for isospin is briefly investigated at the end.