  We present evidence for new, non-trivial RG fixed points with dual magnetic
descriptions in $N=1$ supersymmetric $SP(N_c)$ and $SO(N_c)$ gauge theories.
The $SP(N_c)$ case involves matter $X$ in the antisymmetric tensor
representation and $N_f$ flavors of quarks $Q$ in the fundamental
representation. The $SO(N_c)$ case involves matter $X$ in the symmetric tensor
representation and $N_f$ flavors of quarks $Q$ in the vector representation of
$SO(N_c)$. Perturbing these theories by superpotentials $W(X)$, we find a
variety of interesting RG fixed points with dual descriptions. The duality in
these theories is similar to that found by Kutasov and by Kutasov and Schwimmer
in $SU(N_c)$ with adjoint $X$ and $N_f$ quarks in the fundamental.
