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This paper presents the novel resource allocation scheme for multiclass services in the downlink OFDMA system, in which the frame-based transmission with multiple subchannels and multiple time slots is used. As system utilization and fairness are necessary, the scheme is based on proportional fairness (PF) utility function. Two main service classes are considered. One is the guaranteed service class. The other is the non-guaranteed service class. The scheme guarantees the minimum bit rate for the former class. The PF-based optimization problem with minimum bit rate requirement is formed and solved by using the Lagrange multiplier method with relaxed constraints. The novel PF-based utility function is derived and used for this class. The non-guaranteed class is served after the guaranteed class by using the conventional PF utility function. Extensive simulation with user mobility and finite backlog is conducted. The results show that the proposed scheme is able to satisfy the minimum rate requirement for the guaranteed class with moderate system utilization. Furthermore, within the same class, the scheme can provide very high throughput fairness.