Mobile communication systems beyond the third generation will see the interconnection of heterogeneous radio access networks (UMTS, WiMax, wireless local area networks, etc.) in order to always provide the best quality of service (QoS) to users with multimode terminals. This scenario poses a number of critical issues, which have to be faced in order to get the best from the integrated access network. In this paper, we will investigate the issue of parallel transmission over multiple radio access technologies (RATs), focusing the attention on the QoS perceived by final users. We will show that the achievement of a real benefit from parallel transmission over multiple RATs is conditioned to the fulfilment of some requirements related to the kind of RATs, the multiradio resource management (MRRM) strategy, and the transport-level protocol behaviour. All these aspects will be carefully considered in our investigation, which will be carried out partly adopting an analytical approach and partly by means of simulations. In this paper, in particular, we will propose a simple but effective MRRM algorithm, whose performance will be investigated in IEEE802.11a-UMTS and IEEE802.11a-IEEE802.16e heterogeneous networks (adopted as case studies).