  We perform a numerical study of the QCD corrections to the structure function
$F_L(x,Q^2)$ in the HERA energy range. The $K$--factors are of $O(30%)$ and
larger in parts of the kinematic range. The relative corrections to
$F_L^{c\overline{c}}$ turn out to be scale dependent and partially compensate
contributions to the massless terms.
