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An ASEP with two species of particles and different hopping rates isconsidered on a ring. Its integrability is proved and the Nested AlgebraicBethe Ansatz is used to derive the Bethe Equations for states with arbitrarynumbers of particles of each type, generalizing the results of Derrida andEvans. We present also formulas for the total velocity of particles of a giventype and their limit for large size of the system and finite densities of theparticles.

Algebraic Bethe Ansatz for the two species ASEP with different hopping rates