  We present our recent calculation of the third order corrections to the
semileptonic $b \to c$ and the muon decays. The calculation has been performed
in an expansion around the limit $m_c \sim m_b$, but shows decent convergence
even for $m_c=0$ from which the contribution to the muon decay can be
extracted. For the semileptonic $b \to c$ decay we find large perturbative
corrections in the on-shell scheme which can be significantly reduced by
changing to the kinetic scheme for the bottom quark mass. These results are
important input for the inclusive determination of $|V_{cb}|$ and the Fermi
coupling constant $G_F$.
