A number of years ago, the world of computer networking have witnessed an explosive evolution which continues to rise. In this evolution, the multiple technologies found themselves attracted in an increasingly strong gravity field, generated by the shining star in the computer universe that is known as the Internet. Cognitive Radio (CR) is emerging as one of the key technologies to solve the problem of spectrum scarcity faced by current wireless systems. They are being helplessly directed to a common center, consequently facing a crossroad illustrated by the convergence of numerous networking solutions that have been yet considered mutually exclusives. In our work, we try to approach the problematic related to the optimization of the convergence of two very promising wireless networking technologies which are Wi-Fi and WiMAX. We propose the example of a practical configuration where the two networks converge in a complementary and constructive structure rather than a competitive one. Thus, our contribution is summed in the proposition of a coupling strategy between the access controls in the two networks in the aim of enhancing the global quality of service management in the new composite network. We propose the implementation of that strategy in the form of a combined admission control algorithm that is implemented and verified through simulation, using the specialized free open source software NS-3.