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Flexible resource-allocation (FRA) strategies have been proposed in the literature to mitigate the high blocking rate caused in high-speed mobile communication networks when resource aggregation is used to increase the data rate. In this paper, new FRA strategies that cope with scenarios with multiple service types and multiple priorities are proposed. These are called the FRA strategy with differentiated priorities and quality of service (FRAQoS) and the FRA strategy with prioritized levels (FRASPL). The main distinguishing feature of these strategies is their capacity to prioritize some service types over others. FRAQoS prioritizes the quality of service (QoS) of particular service types over others by introducing the concepts of prioritized call degradation and compensation. However, FRAQoS provides a limited ability to prioritize particular service types over the rest because any incoming call, irrespective of its service type and priority, may trigger resource reallocations to service it. The FRASPL overcomes this limitation by introducing a call-admission mechanism that, when necessary, rejects calls originated by low-priority service types. This enhances the protection to high-priority service types. By prioritizing some services over the others, FRASPL can trade off capacity against QoS. FRAQoS represents particular limiting cases of FRASPL. A mathematical model is developed to investigate the performance of FRAQoS and FRASPL. Then, they are compared with other FRA strategies in a scenario with multiple differentiated service types. Results show that the proposed strategies effectively prioritize service types, providing them with better QoS. This makes FRAQoS and FRASPL specially suitable for class-based QoS provisioning in mobile networks.