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A variety of ordered algebras is a class K of ordered algebras satisfying satisfying a set of inequalities t@?t'. It is shown that a class K of ordered algebras is a variety if K is closed under subalgebras, products, and certain homomorphic images. The process of obtaining a ''canonical'' @w-completion of an ordered algebra is analyzed and it is shown that varieties of ordered algebras are closed with respect to @w-completion. The concluding sections concern (i) a connection between ordered algebras and ordered algebraic theories, and (ii) a logic of inequalities, analogous to equational logic. A completeness theorem for this logic is proved.