Nonlinear equalisers based on minimum BER are proposed for the equalisation of nonlinear time-varying channels. To train the equalisers online, a sliding-window-based hybrid quasi-Newton algorithm is proposed. Switching between sliding-window stochastic gradient algorithm and sliding-window quasi-Newton algorithm makes the new algorithm significantly stabler with a fast convergence rate. Results from extensive simulation tests show that performance of nonlinear equalisers based on minimum BER is better than the equaliser based on minimum mean square error. The proposed algorithm demonstrates high efficiency as well. Copyright © 2013 John Wiley & Sons, Ltd.