We establish a bialgebra theory for anti-flexible algebras in this paper. We introduce the notion of an anti-flexible bialgebra which is equivalent to a Manin triple of anti-flexible algebras. The study of a special case of anti-flexible bialgebras leads to the introduction of anti-flexible Yang-Baxter equation in an anti-flexible algebra which is an analogue of the classical Yang-Baxter equation in a Lie algebra or the associative Yang Baxter equation in an associative algebra. it is unexpected consequence that both the anti-flexible Yang-Baxter equation and the associative Yang-Baxter equation have the same form. A skew-symmetric solution of anti-flexible Yang-Baxter equation gives an anti-flexible bialgebra. Finally the notions of an O-operator of an anti-flexible algebra and a pre-anti-flexible algebra are introduced to construct skew-symmetric solutions of anti-flexible Yang-Baxter equation.
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