Based on Alamouti code, Lee and Williams proposed two-branch transmit diversity block-coded orthogonal frequency-division multiplexing (TDBC-OFDM) systems, namely, space-time block-coded OFDM (STBC-OFDM) and space-frequency block-coded OFDM (SFBC-OFDM). However, they employed the simple maximum-likelihood (SML) detector, which was designed under the assumption that the channel is static over the duration of a space-time/frequency codeword. Therefore, STBC-OFDM/SFBC-OFDM suffers from the high time/frequency selectivity of the wireless mobile fading channel. In this paper, besides the original SML detector, three detectors proposed by Vielmon et al. are applied to improve the two-branch TDBC-OFDM systems. Additionally, assuming sufficient cyclic prefix, the performances of all systems in spatially uncorrelated time-varying multipath Rayleigh-fading channels are evaluated by theoretical derivation and computer simulation, as well. According to the derived bit-error rate (BER), we further derive the bit-error outage (BEO) to provide a more object judgment on the transmission quality within a fading environment. Numerical results have revealed that significant performance improvement can be achieved even when the systems are operated in highly selective channels.