[en] Many models, such as topcolour-assisted technicolour (TC2) models and flavour-universal TC2 models, predict the existence of extra U(1) gauge bosons Z', which couple preferentially to the third generation. The lepton flavour violating (LFV) signals of these new particles at the future e⁺e^- colliders (LCs) are discussed by calculating their contributions to the LFV process e⁺e^- → μτ. We calculate the cross section of this process and discuss its dependence on the beam polarization. The ratio of the signal over the square root of the background (S/√B) is also calculated. The results show that the LFV signals of the gauge bosons Z' may be detected at the future LC experiments