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This paper studies data forwarding in wireless sensor networks (WSNs) where sensor nodes are randomly duty-cycled to save energy. The duty-cycling operation requires the data delivery strategy to be more adaptive for the dynamics caused by the uncertainty of node working schedules. However, the existing maximum-advance routing scheme, at each step the forwarding node selects the node closest to the destination as its next hop forwarder among neighbors, performs poorly in randomly duty-cycled WSNs.In this paper, we propose a new residual time aware (RTA) routing metric for randomly duty-cycled WSNs. RTA is designed to be responsive to the dynamics caused by duty-cycling operation. We also present a residual time aware forwarding (RTAF) strategy using this metric for randomly duty-cycled WSNs. Simulation results demonstrate that our proposed RTAF strategy reduces the retransmissions and delivery delay introduced by the duty-cycling operation. Therefore, it is shown that RTAF increases the data delivery ratio and average advance per hop, and significantly reduces the end-to-end delivery latency.