  Let $(V,q)$ be a vector bundle on a smooth projective curve $X$ together with
a quadratic form $q: \mathrm{Sym}^2(V) \ra \mathcal{O}_X$ (respectively
symplectic form $q: \Lambda^2V \ra \mathcal{O}_X$). Fixing the degeneracy locus
of the quadratic form induced on $V/\ker(q)$, we construct a coarse moduli of
such objects. Further, we prove semi-stable reduction theorem for equivalence
classes of such objects. In particular, the case when degeneracies of $q$ are
higher than one is that of principal interest. We also provide a proof of
properness of polystable orthogonal bundles without appealing to Bruhat-Tits
theory in any characteristic.
