Although each application has its own quality of service (QoS) requirements, the resource allocation for multiclass services has not been studied adequately in multiuser orthogonal frequency division multiplexing (OFDM) systems. In this paper, a total transmit power minimization problem for downlink transmission is examined while satisfying multiclass services consisting of different data rates and target bit-error rates (BER). Lagrangian relaxation is used to find an optimal subcarrier allocation criterion in the context of subcarrier time-sharing by all users. We suggest an iterative algorithm using this criterion to find the upper and lower bounds of optimal power consumption. We also propose a prioritized subcarrier allocation (PSA) algorithm that provides low computation cost and performance very close to that of the iterative algorithm. The PSA algorithm employs subcarrier selection order (SSO) in order to decide which user takes its best subcarrier first over other users. The SSO is determined by the data rates, channel gain, and target BER of each user. The proposed algorithms are simulated in various QoS parameters and the fading channel model. Furthermore, resource allocation is performed not only subcarrier by subcarrier but also frequency block by frequency block (comprises several subcarriers). These extensive simulation environments provide a more complete assessment of the proposed algorithms. Simulation results show that the proposed algorithms significantly outperform existing algorithms in terms of total transmit power consumption.