  The second order casimirs for the affine Krichever--Novikov algebras
$\hat{\mathfrak{gl}}_{g,2}$ and $\hat{\mathfrak{sl}}_{g,2}$ are described. More
general operators which we call semi-casimirs are introduced. It is proven that
the semi-casimirs induce well-defined operators on conformal blocks and, for a
certain moduli space of Riemann surfaces with two marked points and fixed jets
of local coordinates, there is a natural projection of its tangent space onto
the space of these operators. It is (non-formally) explained how semi-casimirs
appear in course of operator quantization of the second order Hitchin
integrals.
