Wireless networks have become an essential part of human life and has opened vast new avenues for education, communication, healthcare, social change and entertainment. Wireless networks offer users many benefits such as portability and flexibility. Hence the constant growth of number of users and demand for wireless network application services has led a constraint on the limited spectrum resources. The resource is scarce and cannot cope or overcome the rapidly growing wireless data traffic. This research aimed at having an adaptive resource allocation scheme that will manage the limited resources in wireless networks and meet the demands of numerous users using cognitive radios. The three wireless network topologies that was considered are relay, mesh and wireless regional area networks. In order to achieve this, throughput maximization scheme by beam scheduling with relay assignment resource allocation for a cognitive radio relay network was developed. Then a subcarrier and power allocation scheme for a cognitive radio multi-relay assisted network was developed to maximize the capacity of its transmission. A model for capacity fairness, power and channel assignment resource allocation in a cognitive radio wireless regional area network was developed. Thereafter, the interference for cognitive radios operating in the television spectrum was minimized through power resource allocation. The route and channel resource in a cognitive wireless mesh network was optimized for capacity maximization. Finally, the shortest end to end path with optimal channel resource allocation for a wireless mesh leased network was determined. The system was found to efficiently access the underutilized spectrum and allocate the limited resources with optimal performance.