The treatments of problems in continuum damage mechanics (CDM) that appear in the scientific literature are based on a number of more or less explicit assumptions. In this paper, these assumptions are reformulated and shown to form a single axiomatic framework of both the "internal variables" and the "multifield continuum" schemes : the fundamental features of both descriptions are thus recognized and correlated with the general principles of mechanics. These developments are based on the general theory of actions developed by . A mathematical foundation for thermodynamics. Archives of Rational Mechanical Analysis 54, 1-104; (1975). On thermodynamics and elastic plastic materials. Archives of Rational Mechanical Analysis 59, 25-51 ;. On thermodynamics of semi-systems with restrictions on the accessibility of states. Archives of Rational Mechanical Analysis 66, 173-181), which is presented in Section 2 in a way slightly different from usual. Then, five axioms for CDM are introduced in Section 3, and related theorems and corollaries are proved, Finally, the Paimgren-Miner's rule of fatigue damage and its limitations are reformulated in the context of the established general framework.