In this thesis, we present a joint maximum likelihood (ML) symbol time and frequency offset estimator for orthogonal frequency division multiplexing (OFDM) systems in multipath rayleigh fading channel. This method uses the cyclic prefix which is contained in symbol and is same to a part of symbol. The estimator which is derived uses the correlation between cyclic prefix and the corresponding part of symbol. In multipath channel, the performance is degraded by ISI. The proposed estimator diminishs the effect of ISI using known channel and signal-to-noise power ratio. The estimator considers the channel and signal-to-noise power ratio. However, it's difficult to know them. We show that we can get the performance similar to the performance obtained by the ML estimators through using a fixed estimator which is obtained by simulation. The frequency offset estimator may be used in a tracking mode and the symbol time estimator in an acquisition mode.