We present in this paper an algebraic approach to the theory of languages of words on countable ordinals. The algebraic structure used, called an Ω₁-semigroup, is an adaptation of the one used in the theory of regular languages of Ω-words. We show that finite Ω₁-semigroups are equivalent to automata. In particular, the proof gives a new algorithm for determinizing automata on countable ordinals. As in the cases of finite and Ω-words, a syntactic Ω₁-semigroup can effectively be associated with any regular language of words on countable ordinals. This result is used to prove an Eilenberg type theorem. There is a one-to-one correspondence between varieties of Ω₁-languages and pseudo-varieties of Ω₁-semigroups.