As basic as the phonemic principle is to linguistic science, it is only quite recently that it has had the serious attention of linguists. In studying the phonemes of Chitimacha (an Indian language of Louisiana) I knew of no single source from which I could learn to understand all the phenomena that I observed. There seemed to be a need for an adequate and complete exposition of the phonemic principle including, especially, an account of how it applies to the more marginal and difficult types of phenomena. I at first intended to include this discussion in my paper on the Chitimacha phonemes, but the wider interest of the general discussion makes it more appropriate that it be published separately. The specific treatment of Chitimacha, which can now appear without theoretical digressions, will serve to illustrate many of the points discussed here. I do not attempt to cite previous authors on all of the points treated in this paper, though I recognize fully my dependence on them. On a few points my treatment attempts to avoid weaknesses in previous treatments, and a point or two are perhaps introduced here for the first time. However, the chief ideals of this paper are theoretical comprehensiveness, consistency of treatment, and brevity.