This study is concerned with the challenging and timely problem of channel equalisation and data detection for orthogonal frequency division multiplexing (OFDM) systems in the presence of frequency-selective and very rapidly time-varying channels. The algorithm is based on the space alternating generalised expectation-maximisation (SAGE) technique which is particularly well suited to multicarrier signal formats and can be easily extended to multi-input multi-output-OFDM systems. In fast fading channels, the orthogonality between subcarriers is destroyed by the time variation of a fading channel over an OFDM symbol duration which causes severe inter-carrier interference (ICI) and, in conventional frequency-domain approaches, results in an irreducible error floor. The proposed joint data detection and equalisation algorithm updates the data sequences in series leading to a receiver structure that also incorporates ICI cancellation, enabling the system to operate at high vehicle speeds. A computational complexity investigation as well as detailed computer simulations indicate that this algorithm has significant performance and complexity advantages over existing suboptimal detection and equalisation algorithms proposed earlier in the literature.