Joint bandwidth and power allocation for a multi-radio access(MRA)system in a heterogeneous wireless access environment is studied.Since both the number of users being served by the system and the wireless channel state are time-varying,the optimal resource allocation is no longer a static optimum and will change with the varying network state.Moreover,distributed resource allocation algorithms that require iterative updating and signaling interactions cannot converge in negligible time.Thus,it is unrealistic to assume that the active user number and the wireless channel state remain unchanged during the iterations.In this paper,we propose an adaptive joint bandwidth and power allocation algorithm based on a novel iteration stepsize selection method,which can adapt to the varying network state and accelerate the convergence rate.A distributed solution is also designed for the adaptive joint resource allocation implementation.Numerical results show that the proposed algorithm can not only track the varying optimal resource allocation result much more quickly than a traditional algorithm with fixed iteration stepsize,but can also reduce the data transmission time for users and increase the system throughput. Joint bandwidth and power allocation for a multi-radio access (MRA) system is in a heterogeneous wireless access environment is studied. Both both the number of users being served by the system and the wireless channel state are time-varying, the optimal resource allocation is is no longer a static optimum and will change with the varying network state. Mobile, distributed resource allocation algorithms that require iterative updating and signaling interactions can not converge in negligible time .hus, it is unrealistic to assume that the active user number and the wireless channel state remain unchanged during the iterations.In this paper, we propose an adaptive joint bandwidth and power allocation algorithm based on a novel iteration stepsize selection method, which can adapt to the varying network state and accelerate the convergence rate. A distributed solution is also designed for the adaptive joint resource allocation implementation. Numerical results show that the proposed algorithm can not on ly track the varying optimal resource allocation result much more quickly than a traditional algorithm with fixed iteration stepsize, but also also reduce the data transmission time for users and increase the system throughput.