By applying the differential space-time block code (DSTBC) to wireless multicarrier transmission, Diggavi et al. were the first to propose the two-input-multiple-output (2IMO) differentially space-time-time block coded OFDM (TT-OFDM) system. In this paper, we propose three novel differentially transmit-diversity block coded OFDM (DTDBC-OFDM) systems, namely, the FT-, FF-, and TF-OFDM systems. For instance, the TF-OFDM stands for the differentially space-time-frequency block coded OFDM. Moreover, the noncoherent maximum-likelihood sequence detector (NSD), and its three special cases, namely, the noncoherent one-shot detector, the linearly predictive decision-feedback (DF) detector, and the linearly predictive Viterbi receiver are incorporated to the 2IMO DTDBC-OFDM systems. Furthermore, a simple closed-form BER expression for the systems utilizing the noncoherent one-shot detector in the time-varying multipath Rayleigh fading channels is given. Numerical results have revealed that 2IMO DTDBC-OFDM systems employing the noncoherent one-shot detector can obtain significant performance improvement. However, when few antennas are available, the implementation of the linearly predictive DF detector or the linearly predictive Viterbi receiver is necessary for achieving better performance.