  We study the algebra of difference operators that commute with the two-body
Ruijsenaars operator, a $q$-deformation of the Lam\'e differential operator,
for generic values of the deformation parameter. The algebra is commutative. It
is the algebra of polynomial functions on an affine hyperelliptic curve
$Y^2=P(X^2)$. We also compute the difference Galois group of the eigenvalue
problem.
