Abstract: In this paper, by using partial order method, the existence and uniqueness of solutions for systems of a class of abstract operator equations in Banach spaces are studied. The results obtained in this paper improve and unify many recent results. Applications to the system of nonlinear integral equations in Banach space are given. It is proved that the unique solution exists by the
iterative sequence which converges to the unique solution is constructed and the error estimate is given.

Key words: Systems of abstract operator equations, Unique solution, Iterative sequences, Systems of integral