In this paper, we investigate the power and rate-control schemes for multiple cognitive radio (CR) links in the same neighborhood, which operate over multiple channels (frequency bands) in the presence of licensed primary radios (PRs) with a delay constraint imposed on data transmission. By further considering a practical delay in spectrum sensing, an efficient algorithm is proposed to maximize the average sum rate of the CR links over a finite time horizon under the constraints on the CR-to-PR interference and the average transmit power for each CR link. In the proposed algorithm, the PR occupancy of each channel is modeled as a discrete-time Markov chain (DTMC). Based on such a model, a novel power and rate control strategy based on dynamic programming (DP) is derived, which is a function of the delayed spectrum sensing output, the instantaneous channel gains for the CR links, and the remaining power budgets for the CR transmitters. Simulation results show that the proposed algorithm leads to a significant performance improvement over three heuristic algorithms discussed in this paper.