In OFDM systems, significant performance degradation can result from a small carrier frequency offset, which may occur due to drift after an initial frequency acquisition. We consider the estimation of the frequency offset in the tracking mode, using demodulation decisions rather than training sequences. Both maximum-likelihood estimation and a simpler, iterative technique are considered. For a system with 128 subchannels, coherent QPSK modulation, and an exponentially decaying multipath-fading channel, our simulation results show that unbiased estimation with a standard deviation less than 1% can he achieved within three iterations if the frequency offset is less than 15%. After the correction using the estimated frequency offset, the bit error rate of demodulation decisions is no different from that without a frequency offset.