We consider the scenario in which multiple transmitters send signals to a receiver in the asynchronous multiple-input-multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM) mode. A receiver structure that can perform joint synchronization and space-time equalization for the asynchronous MIMO-OFDM systems is proposed. We first introduce a novel space-time equalization algorithm based on the channel state information. This algorithm aims to null the cochannel interference and combat asynchronism, as well as minimize a lower bound to the symbol error rate in the asynchronous MIMO-OFDM system. In the second part of this paper, we propose a training-based minimizing mean-square-error (MMSE) algorithm to jointly obtain frequency offsets and equalization delays. We compensate for the effects of the frequency offsets and the propagation delays with these estimated parameters and then use the proposed direct training-based equalizer design algorithm to obtain the equalizer coefficients. The simulation section illustrates the desirable bit-error-rate (BER) performance of our proposed algorithms.