  We find the defining structures of two-parameter quantum groups
$U_{r,s}(\frak g)$ corresponding to the orthogonal and the symplectic Lie
algebras, which are realized as Drinfel'd doubles. We further investigate the
environment conditions upon which the Lusztig's symmetries exist between
$(U_{r,s}(\frak g), < ,>)$ and its associated object $(U_{s^{-1}, r^{-1}}(\frak
g), < | >)$.
