  The most important part of the order $\alpha_s^2$ corrections to the charm
component of the charged-current structure functions $F_2(x,Q^2)$ and
$F_3(x,Q^2)$ have been calculated. This calculation is based on the asymptotic
form of the heavy-quark coefficient functions corresponding to the higher order
corrections to the W-boson-gluon fusion process. These coefficient functions
which are in principle only valid for $Q^2 \gg m^2$ can be also used to
estimate the order $\alpha_s^2$ contributions at lower $Q^2$ values provided $x
< 0.1$. It turns out that the above corrections are appreciable in the large
$Q^2$-region and they explain the discrepancy found for the structure functions
between the fixed-flavour scheme (FFS) and the variable-flavour-number scheme
(VFNS). These corrections also hamper the extraction of the strange-quark
density from the data obtained for the charged-current and the
electromagnetic-current processes.
