  We study the local structure of the singularity in the moduli space of
sheaves on a K3 surface which has been resolved by K O'Grady in his
construction of new examples of hyperkaehler manifolds. In particular, we
identify the singularity with the closure of a certain nilpotent orbit in the
coadjoint representation of the group $Sp(4)$. We also prove that the moduli
spaces for some other sets of numerical parameters do not admit a smooth
symplectic resolution of singularities.
