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Intermittently connected mobile networks are wireless networks where most of the time there does not exist a complete path from source to destination, or such a path is highly unstable and may break soon after it has been discovered. In this context, conventional routing schemes would fail. To deal with such networks we propose the use of an opportunistic hop-by-hop routing model. According to the model, a series of independent, local forwarding decisions are made, based on current connectivity and predictions of future connectivity information diffused through nodes' mobility. The important issue here is how to choose an appropriate next hop. To this end, we propose and analyze via theory and simulations a number of routing algorithms. The champion algorithm turns out to be one that combines the simplicity of a simple random policy, which is efficient in finding good leads towards the destination, with the sophistication of utility-based policies that efficiently follow good leads. We also state and analyze the performance of an oracle-based optimal algorithm, and compare it to the online approaches. The metrics used in the comparison are the average message delivery delay and the number of transmissions per message delivered.