vacua (and independent tests) than unknown functions, the agreement of the resulting structures with duality in all vacua is a non-trivial check.

In section [*2*]{} we review the results of . We describe the class of theories we will study, describe the duality map, and discuss their classical and quantum chiral rings and moduli spaces of vacua. In particular we establish the existence of new quantum relations in the chiral rings of these theories corresponding to classical relations in the duals.

In section [*3*]{} we construct the detailed map of the superpotential . We describe the transformation of coordinates $\{s\}\to \{t\}$ and show that the duality map is rather simple in the $\{t\}$ coordinates. After constructing this map we change coordinates back to the physically natural ones.

In section [*4*]{} we turn to the gauge coupling constant matching relation . We show that it is preserved under the various deformations. In particular, with arbitrary coupling constants $t_i$ one can compute the effective Lagrangian of the low energy theory both in the electric and in the magnetic variables. These lead (generically) to dual pairs of supersymmetric QCD like theories whose scales are related by the appropriate scale matching relation. The couplings 