For CR systems, where primary and CR users co-exist in adjacent bands, it is important to keep the interference introduced to the primary user (PU) band within a tolerable range. In this paper, we investigate the subcarrier and power allocation problem in CR systems, where primary and CR users co-exist in adjacent bands, while keeping the total interference introduced to the PU band below a certain threshold and the total power allocated to the CR users under a constraint. First, according to the different purposes of the resource allocation, several suboptimal subcarrier allocation algorithms are investigated, which are termed as Max-Rate, Min-Interference and Fair-Rate subcarrier allocation algorithm, separately. Further, for a given subcarrier allocation three suboptimal power allocation algorithms which have less complexity are proposed and compared to the optimal power allocation algorithm. Numerical results are obtained for the behaviors and performance of our proposed algorithms.