  To each representation of the elliptic quantum group $E_{\tau,\eta}(sl_2)$ is
associated a family of commuting transfer matrices. We give common eigenvectors
by a version of the algebraic Bethe ansatz method. Special cases of this
construction give eigenvectors for IRF models, for the eight-vertex model and
for the two-body Ruijsenaars operator. The latter is a $q$-deformation of
Hermite's solution of the Lam\'e equation.
