This paper deals with the performance analysis of Alamouti coded orthogonal frequency division multiplexing (OFDM) systems over time-varying multipath Rayleigh fading channels. In our analysis, we consider a physically more realistic channel, which can be correlated either in time or in space or even in both domains. We derive an analytical expression for the bit error probability (BEP), which describes the performance of an Alamouti coded OFDM system over fading channels correlated in space and time. It is shown that the derived BEP can be reduced to the known BEP obtained over fading channels correlated in time or space. The correctness of all theoretical results is validated by system simulations. The knowledge of the obtained theoretical results makes the BEP evaluation more straightforward and less time-consuming compared to simulations. Moreover, it allows us to discuss the effect of the maximum Doppler frequency and the antenna spacing on the system performance.