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The majority of control techniques for nonlinear systems are based on state-space description, the problem of finding state-space realization of input-output system is an important task. This paper is devoted to the problem of realizability of the interconnections of the nonlinear discrete- time input-output systems. Necessary and sufficient conditions are given for the existence of a state-space realization for the cases of series and parallel interconnections of the systems represented by the input-output difference equation. Constructive (up to integrating differential one forms) procedures to obtain a realizations for such composite systems are given.