This paper proposes and analyzes cognitive multihop decode-and-forward networks in the presence of interference due to channel estimation errors. To reduce interference on the primary network, a simple yet effective back-off control power method is applied for secondary multihop networks. For a given threshold of interference probability at the primary network, we derive the maximum back-off control power coefficient, which provides the best performance for secondary multihop networks. Moreover, it is shown that the number of hops for secondary network is upper-bounded under the fixed settings of the primary network. For secondary multihop networks, new exact and asymptotic expressions for outage probability (OP), bit error rate (BER) and ergodic capacity over Rayleigh fading channels are derived. Based on the asymptotic OP and BEP, a pivotal conclusion is reached that the secondary multihop network offers the same diversity order as compared with the network without back off. Finally, we verify the performance analysis through various numerical examples which confirm the correctness of our analysis for many channel and system settings and provide new insight into the design and optimization of cognitive multihop networks.