We develop synchronization algorithms for both the downlink and the uplink of quasi-synchronous and asynchronous orthogonal frequency division multiple access systems. Unlike existing alternatives, the proposed time- and carrier-offset estimators do not require the transmission of known sequences and exhibit performance independent of the underlying channel zero locations. The only necessary assumption is that there are virtual subcarriers which are not occupied by any user. We derive a closed-form variance expression for the carrier-offset estimator at high signal-to-noise ratio (SNR), as a function of the number of active users and the SNR. We compare our method with alternative ones and validate our theoretical derivations with simulation results.