  We report on the calculation of the factorisable one-loop weak-interaction
corrections to the initial and final states for three-jet observables in
electron-positron annihilations. We show that such corrections are of a few
percent at $\sqrt s=M_Z$. Hence, while their impact is not dramatic in the
context of LEP1 and SLC, where the total error on the measured value of
$\alpha_{\mathrm{S}}$ is larger, at a future Linear Collider, running at the
$Z$ mass peak (e.g., GigaZ), they ought to be taken into account in the
experimental fits, as here the uncertainty on the value of the strong coupling
constant is expected to be at the 0.1% level or even smaller. The calculation
has been performed using helicity amplitudes so that it can be applied to the
case of polarised beams.
