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This paper investigated the couple-group consensus problems of the multiagent networks with the influence of communication and input time delays. Based on the frequency-domain theory, some algebraic criteria are addressed analytically. From the results, it is found that the input time delays and the coupling strengths between agents of the systems play a crucial role in reaching group consensus. The convergence of the system is independent of the communication delays, but it will affect the convergence rate of the system. Finally, several simulated examples are provided to verify the validity and correctness of our theoretical results.