Offset-QAM-based filterbank multicarrier (FBMC-OQAM) has been shown to be a promising alternative to cyclic prefix-orthogonal frequency division multiplexing for the future generation of wireless communication systems. Unfortunately, as the channel gets more selective in time and frequency, the FBMC-OQAM orthogonality is progressively destroyed and distortion appears after the demodulation process at the receiver. While channel frequency selectivity has been very widely studied in the FBMC literature, the impact of time selectivity of the channel has not received that much attention. In this paper, the effect of the two types of selectivity on a multiple-input multiple-output (MIMO) FBMC system is characterized and a parallel equalization structure that can compensate for the doubly dispersive nature of the channel is proposed. This design uses multiple analysis filterbanks and extends previous approaches that were dealing only with channel frequency selectivity. A theoretical approximation of the remaining distortion after equalization is given. The study is performed for a general MIMO system but can also be particularized to single-input single-output systems. Simulation results demonstrate the high efficiency of the proposed receiver structure and the accuracy of the theoretical approximations is verified. © 2017 IEEE.