  We discuss electric-magnetic duality in two new classes of supersymmetric
Yang-Mills theories. The models have gauge group $Sp(2\nc)$ or $SO(\nc)$ with
matter in both the adjoint and defining representations. By perturbing these
theories with various superpotentials, we find a variety of new infrared fixed
points with dual descriptions. This work is complementary to that of Kutasov
and Schwimmer on $SU(\nc)$ and of Intriligator on other models involving
$Sp(2\nc)$ and $SO(\nc)$.
