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Signal transmission characteristics of some multilayer graphene nano-ribbon (MLGNR) interconnects are studied in this paper, with an equivalent single-conductor (ESC) model implemented for the analysis of their transient responses. In this model, both capacitive and inductive couplings between adjacent GNR layers are treated appropriately. According to the derived transfer function using the fourth-order approximation, the output voltage waveforms are predicted for both 14- and 22-nm technology nodes. In particular, the effects of Fermi level of MLGNR on the time delay of the transmitted rectangular pulse are examined and compared. Based on the decoupled partially differential equations (PDEs) for the common and differential modes of voltage wave propagation in the edge-coupled MLGNR interconnects, their output voltage responses are also predicted for different technology nodes, which are useful for the evaluation of on-chip signal integrity or EMC and EMI issues of MLGNR-built transmission lines for the future ICs.