In this work, we study a cooperative network with multiple full-duplex buffer-aided relays. A hybrid cooperative relaying policy is proposed that employs power adaptation and consists of two alternative schemes: (i) full-duplex transmission through the relay which requires the least total power expenditure and loop interference is mitigated through power adaptation; (ii) buffer-aided max − link selection with power adaptation, when full-duplexity is not feasible. Aiming to reduce the overhead of channel state information (CSI) acquisition and processing, we propose a suboptimal distributed method for relay selection, for which the network performance is not degraded significantly. We show that power adaptation offers reduced overhead of CSI acquisition. Numerical results and comparisons with other state-of-the-art relaying schemes are provided and performance evaluation in terms of throughput, power minimization and switching rate, show the benefits of the proposed hybrid scheme.Index Terms-Cooperative networks, full-duplex, opportunistic relaying, buffer-aided relays, hybrid relay selection.