We discuss electric-magnetic duality in two new classes of supersymmetric Yang-Mills theories. The models have gauge group $Sp(2 c)$ or $SO( c)$ 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 $SU( c)$ and of Intriligator on other models involving $Sp(2 c)$ and $SO( c)$.
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