In this contribution, the convergence behaviour of the adaptive linear equaliser based on subband decomposition technique is investigated. Two different subband-based linear equalisers are employed, with the aim of improving the equaliser's convergence performance. Simulation results over three channel models having different spectral characteristic are presented. Computer simulations indicate that subband-based equalisers outperform the conventional fullband linear equaliser when channel exhibit severe spectral dynamic. Convergence rate of subband equalisers are governed by the slowest subband, whereby different convergence behaviour in each individual subband is observed. Finally, the complexity of fullband and subband equalisers is discussed.