Due to the uncertainty of transmission opportunities between mobile nodes, the routing of delay-tolerant networks (DTNs) exploits the mechanism of opportunistic forwarding. Efficient algorithms and policies for opportunistic forwarding are crucial for maximizing the message delivery probability while reducing the delivery cost. In this paper, we investigate the problem of energy-efficient opportunistic forwarding for DTNs. First, we model the message dissemination by introducing a continuous-time Markov framework. Based on this framework, we formulate the optimization problem of opportunistic forwarding, with the constraint of energy consumed by the message delivery for both two-hop and epidemic forwarding. Then, based on the solution of the optimization problem, we design different kinds of forwarding policies such as static and dynamic policies. Among these policies, we find that the threshold dynamic policy is optimal for both two-hop and epidemic forwarding. By simulation results, we show the accuracy of our continuous-time Markov analysis model. Furthermore, through extensive numerical results, we demonstrate that the performance of the threshold dynamic policy is the best among the static and continuous dynamic policies, and among the continuous dynamic policies, the negative-power policy provides relatively better performance.