Dynamic schemes for downlink packet radio resource management (RRM) are the topic of this paper. The concept of PARPS (Packet And Resource Plan Scheduling) is introduced. PARPS reduces the combined proble m of dynamic RRM, including statistical multiplex, dynamic channel allocation, power control, link adaptation, reuse partitioning, soft handover, admission control, etc, to a scheduling problem. PARPS makes it possible to achieve dynamic RRM individually for each data packet, without performing signal-to-interference ratio calculations for every single packet. A PARPS algorithm assigns a so-called resource plan to each timeslot, and assigns data packets to timeslots and transmitters. A resource plan is a combination of several radio parameters, e.g. transmitter power levels, coding rates and modulation schemes, for a group of centrally controlled and synchronised transmitters. We propose several optimised and heuristic PARPS algorithms. Optimised PARPS is NP hard, i.e. it is not realistic to solve in real time for a big system, but it can be used for finding an upper bound for the compound effect of several RRM techniques by means of computer simulations. The heuristic algorithms are realistic to implement in real systems. Our results show that some of the heuristic algorithms have delay performance very near an optimised algorithm, and that the capacity and coverage of a set of resource plans for 2D Poisson traffic can be evaluated with static analyses, i.e. without queuing system simulation. We apply PARPS to cellular systems based on the COFDM modulation scheme. Especially, we have personal communication services in the MEMO system in mind, where the terrestrial digital audio or video broadcasting system (DAB or DVB-T) is used as a broadband downlink, in combination with some narrowband uplink, e.g. GSM.