This study investigates the downlink resource allocation problem in orthogonal frequency division multiple access heterogeneous networks consisting of macrocells and femtocells sharing the same frequency band. The focus is to devise optimised policies for femtocells' access to the shared spectrum, in terms of femtocell transmissions, in order to maximise femto‐users (FUEs) sum data rate while ensuring that certain level of quality of service (QoS) for the macro‐cell users in the vicinity of femtocells is provided. The optimal solution to this problem is obtained by employing the well‐known dual Lagrangian method and the optimal femtocell transmit power and resource allocation solution is derived in detail. However, the optimal solution introduces high computational complexity. To this end, a heuristic solution to the problem is proposed. The algorithms to implement both optimal and efficient suboptimal schemes in a practical system are also given in detail while their complexity is compared. Simulation results show that proposed dynamic resource allocation scheme (a) ensures the macro‐users QoS requirements compared with the Reuse‐1 scheme, where femtocells are allowed to transmit at full power and bandwidth; (b) can maintain FUE data rates at high levels; (c) provides performance close to the optimal solution, while introducing much lower complexity.