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The model following control problem is addressed for a class of nonlinearly interconnected systems with time delays. The subsystems are with multiple dead-zone actuators and mismatched time-varying disturbances. To deal with the multiple unknown dead-zone inputs, we decompose the system properly based on the input matrix. By using the adaptive method to compensate the unknown parameters, we design a new and simple memoryless controller. The stability of the resultant closed-loop error system is proved by employing a new Lyapunov Krasovskii functional. The designed controller is tolerant to any dead-zone inputs and general time delays. Finally, the simulations are performed and the results show the potential of the proposed method.