  Let $C$ be an algebraic curve of genus $g$ and $L$ a line bundle over $C$.
Let $\mathcal{MS}_C(n,L)$ and $\mathcal{MO}_C(n,L)$ be the moduli spaces of
$L$-valued symplectic and orthogonal bundles respectively, over $C$ of rank
$n$. We construct rational curves on these moduli spaces which generalize Hecke
curves on the moduli space of vector bundles. As a main result, we show that
these Hecke type curves have the minimal degree among the rational curves
passing through a general point of the moduli spaces. As its byproducts, we
show the non-abelian Torelli theorem and compute the automorphism group of
moduli spaces.
