Introduction. In a series of papers [l-4] Halmos introduced the theory of homogeneous polyadic algebras. These polyadic algebras correspond to first order calculi in which there is only one sort of variables. The purpose of this paper is to introduce the theory of nonhomogeneous polyadic algebras, the latter algebras corresponding to first order calculi in which there are several sorts of variables; these calculi were first treated in [6; 7]. In §1, we develop the general theory; in §2, we

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... a representation theorem which proof, even in the homogeneous case, is of some novelty; finally, in §3, we show that, to a certain extent, the theory of finite-sorted nonhomogeneous algebras can be reduced to that of homogeneous algebras.