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In this work, we focus on iterative distributed model predictive control (DMPC) of large-scale nonlinear systems subject to delayed state feedback. The motivation for studying this control problem is the presence of delayed measurements in feedback control of large-scale chemical processes and the potential use of sensors and actuators in industrial applications to improve closed-loop performance. Under the assumption that there exists an upper bound on the maximum measurement delay, we design an iterative DMPC system for nonlinear systems subject to delayed state feedback. The design takes advantage of bi-directional communication between the distributed controllers used in the iterative DMPC system. Sufficient conditions under which the proposed distributed control design guarantees that the states of the closed-loop system are ultimately bounded in a region that contains the origin are provided. The theoretical results are illustrated through a catalytic alkylation of benzene process.