  We investigate the finite-dimensional representation theory of two-parameter
quantum orthogonal and symplectic groups that we found in [BGH] under the
assumption that $rs^{-1}$ is not a root of unity and extend some results [BW1,
BW2] obtained for type $A$ to types $B$, $C$ and $D$. We construct the
corresponding $R$-matrices and the quantum Casimir operators, by which we prove
that the complete reducibility Theorem also holds for the categories of
finite-dimensional weight modules for types $B$, $C$, $D$.
