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In this paper, we study the impact of time-selective fading on quasi-orthogonal space-time (ST) coded orthogonal frequency-division multiplexing (OFDM) systems over frequency-selective Rayleigh fading channels. OFDM is robust against frequency-selective fading, but it is more vulnerable to time-selective fading than single-carrier systems. In ST-OFDM, channel time variations cause not only intercarrier interference among different subcarriers in one OFDM symbol, but also intertransmit-antenna interference. We quantify the impact of time-selective fading on the performance of quasi-orthogonal ST-OFDM systems by deriving, via an analytical approach, the expressions of carrier-to-interference and signal-to-interference-plus-noise ratios. We observe that system error performance is insensitive to changes in vehicle speeds and the channel power-delay profile, but very sensitive to changes in the number of subcarriers. We also evaluate the performance of five different detection schemes in the presence of time-selective fading. We show that although there exist differences in their relative performances, all these detection schemes suffer from an irreducible error floor.