Joint relay-selection and power-allocation strategies are devised to prolong the lifetime of amplify-and-forward (AF) cooperative networks. Lifetime is defined as the time duration within which the desired signal-to-noise ratio (SNR) at the destination is met with a certain probability. Based on selective relaying, we propose three strategies that take into account the local channel state information (CSI) and the local residual energy information (REI) at each relay to prolong the network lifetime. With a finite number of power levels, the energy dissipation process can be modeled as a finite-state Markov chain and the optimal lifetime maximization strategy can be derived using dynamic programming. We demonstrate that the network lifetime can be extended considerably by exploiting both CSI and REI via numerical simulation. The performance of the proposed strategies that utilize only local CSI and REI is shown to be comparable to that of the optimal strategy that demands global CSI and REI.