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As Wi-Fi handheld devices providing a variety of data and multimedia services become more widespread, and as the global demand for internet access everywhere rapidly increases, energy-efficient network mobility (NEMO) technology is attracting great attention with respect to the latest research in mobile networking. The previous research relating to energy-efficient networks in mobile networking has focused on routing protocol or topology control. In NEMO, cost-efficient protocol design reduces unnecessary costs because of mobility signalling and packet delivery, and saves limited network bandwidth in both wired and especially wireless, which is one of the important issues of energy efficiency. In this study, the authors propose a cost-efficient proxy router-based NEMO scheme (PR-NEMO) providing efficient mobility management and packet delivery method. In PR-NEMO, a mobile network is formed with a unique ID and the information of mobile network nodes (MNNs) within the mobile network anchored at local mobility anchor (LMA) are distributed to attached mobile access gateway (MAG). The authors analyse the performance of the PR-NEMO with the N-PMIPv6 and the rNEMO in terms of total cost; that is, sum of location update cost and packet-tunnelling cost. Numerical results demonstrate that the PR-NEMO is the most cost-efficient scheme, under various conditions, among the three schemes evaluated.