  Of the the three best-measured electroweak observables, $\alpha$, $G_\mu$ and
$M_Z$, the first two are extracted from low-energy processes. Both $G_\mu$ and
$M_Z$ are now known to an accuracy of about 2 parts in $10^5$ and there is a
proposal to improve the measurement of the muon lifetime by a factor of 10 in
an experiment at Brookhaven. Yet calculations of electroweak radiative
corrections currently do no better than a few parts in $10^3$--$10^4$ and
therefore cannot exploit to available experimental precision. We report on the
calculation of the ${\cal O}(N_f\alpha^2)$ corrections to Thomson scattering
and the muon lifetime from which $\alpha$ and $G_\mu$, respectively, are
obtained. The ${\cal O}(N_f\alpha^2)$ corrections are expected to be a dominant
gauge-invariant subset of 2-loop corrections.
