This paper investigates the effect of channel estimation errors on the capacity of full-duplex amplify-and-forward relay networks. We first derive the lower bound of the capacity in the presence of channel estimation errors and residual self-interference due to full-duplex relaying. Accordingly, the optimal power allocation schemes in maximizing the capacity with joint power constraints are proposed for single-relay and multi-relay networks. Furthermore, optimal and suboptimal algorithms for joint relay selection and power allocation are provided for the comparison. Simulation results show the performance gains of the proposed algorithms versus per-node transmit power and relay-node number, and point out the significant effects of channel estimation errors and relay positioning on full-duplex cooperative