  We give a solution of the Inverse Scattering Problem for integrable systems
with a finite number degrees of freedom, admitting a Lax representation with
spectral parameter on a Riemann surface. While conventional approaches deal
with the systems with $GL(n)$ symmetry, we focus on the problems arising in the
case of symmetry with respect to a semi-simple group. Our main results apply to
Hitchin systems of the types $B_n$, $C_n$, $D_n$.
