  Let $(Q,\sigma)$ be a symmetric quiver, where $Q=(Q_0,Q_1)$ is a finite
quiver without oriented cycles and $\sigma$ is a contravariant involution on
$Q_0\sqcup Q_1$. The involution allows us to define a nondegenerate bilinear
form $<,>$ on a representation $V$ of $Q$. We shall call the representation
orthogonal if $<,>$ is symmetric and symplectic if $<,>$ is skew-symmetric.
Moreover we can define an action of products of classical groups on the space
of orthogonal representations and on the space of symplectic representations.
For symmetric quivers of finite type, we prove that the rings of
semi-invariants for this action are spanned by the semi-invariants of
determinantal type $c^V$ and, in the case when matrix defining $c^V$ is
skew-symmetric, by the Pfaffians $pf^V$.
