After the example of the extended electroweak models, which predict the existence of the heavy neutral vector boson Z′, we discuss, for the e+e− linear colliders of the new generation, the possibilities of searching for the extra boson effects provided that various configurations of the beam polarizations will be available. For the most popular models [E6-superstring-inspired, LR- and Y(YL)-composite models] we show that realization of the specific beam polarizations can substantially enhance the experiment sensitivity to the Z′ signal in comparison with the case of the unpolarized beams.