In this paper, two optimal power allocation strategies for hybrid interweave-underlay cognitive cooperative radio networks (CCRNs) are proposed to maximize channel capacity and minimize outage probability. The proposed power allocation strategies are derived for the case of Rayleigh fading taking into account the impact of imperfect spectrum sensing on the performance of the hybrid CCRN. Based on the optimal power allocation strategies, the transmit powers of the secondary transmitter and secondary relay are adapted according to the fading conditions, the interference power constraint imposed by the primary network (PN), the interference from the PN to the hybrid CCRN, and the total transmit power limit of the hybrid CCRN. Numerical results are provided to illustrate the effect of the interference power constraint of the PN, arrival rate of the PN, imperfect spectrum sensing, and the transmit power constraint of the hybrid CCRN on channel capacity and outage probability. Finally, comparisons of the channel capacity and outage probability of underlay, overlay, and hybrid interweaveunderlay CCRNs are presented to show the advantages of the hybrid spectrum access. OAPA