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For 10GBASE-T systems, variation in a multiple-input-multiple-output (MIMO) channel degrades the decision-point signal-to-noise ratio (DP-SNR) owing to imperfect pre-equalisation in the Tomlinson-Harashima precoding (THP) at the transmitter sides and catastrophic error propagation in far-end crosstalk (FEXT) cancellation at the receiver sides. Moreover, by using fixed THP coefficients during data transmission, as specified in the 10GBASE-T standard, and the non-linearity of THP pose challenges in the design of adaptive receivers. The authors propose an adaptive two-stage equalisation and FEXT cancellation (TS-EFC) architecture without updating the THP coefficients to combat channel variation at both the transmitter and receiver sides. In the first stage, we propose a new non-decision-directed FEXT canceller at the transmitter side using a joint training architecture to avoid error propagation. In the second stage, we devise an adaptive MIMO equaliser together with a novel pre-processing unit at the receiver side to combat channel variation. The pre-processing unit can eliminate the non-linearity issue by estimating both effective data sequences and precoded channel inputs. In addition, we develop a block least mean square algorithm that exploits the properties of two-dimensional modulated symbols for updating coefficients of the adaptive MIMO equaliser. Simulation results show that our TS-EFC architecture is robust against channel variation and significantly improves the DP-SNR. It eliminates the error propagation and also achieves faster convergence rates during the adaptation process.