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We give one parameter deformation of level $k$ free field realization of thescreening current of the elliptic algebra $U_{q,p}(sl_2^)$. By means of thesefree field realizations, we construct infinitly many commutative operators,which we call the nonlocal integrals of motion associated with level $k$realization of the elliptic algebra $U_{q,p}(sl_2^)$. They are given asintegrals involving a product of the screening current and elliptic thetafunctions. This paper give level $k$ generalization of the nonlocal integralsof motion given in [arXiv:0705.0427].

A remark on the integrals of motion associated with level $k$ realization of the elliptic algebra $U_{q,p}(sl_2^)$