  We discuss the renormalization of the electric charge at the two-loop level
in the Standard Model of the electroweak interactions. We explicitly calculate
the expression of the complete on-shell two-loop counterterm using the
Background Field Method and discuss the advantages of this computational
approach. We consider the related quantity $\hat e(\mu)$, defined in the $\ms$
renormalization scheme and present numerical results for different values of
the scale $\mu$. We find that the full 2-loop electroweak corrections
contribute more than 10 parts in units $10^{-5}$ to the $\Delta \hat\alpha
(\mz^2)$ parameter, obtaining $\hat\alpha^{-1}(\mz)= 128.12 \pm 0.05$ for
$\Delta\alpha_{had}(\mz^2) =0.027572 \pm 0.000359$.
