  We explicitly construct two classes of infinitly many commutative operators
in terms of the deformed W-algebra $W_{qt}(sl_N^)$, and give proofs of the
commutation relations of these operators. We call one of them local integrals
of motion and the other nonlocal one, since they can be regarded as elliptic
deformation of local and nonlocal integrals of motion for the $W_N$ algebra.
