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We implement the Bethe anstaz method for the elliptic quantum group$E_{\tau,\eta}(A_2^{(2)})$. The Bethe creation operators are constructed aspolynomials of the Lax matrix elements expressed through a recurrence relation.We also give the eigenvalues of the family of commuting transfer matricesdefined in the tensor product of fundamental representations.

Algebraic Bethe ansatz for the elliptic quantum group $E_{\tau,\eta}(A_2^{(2)})$