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We examine the models with gauge group U(1)(k-1) x Pi(i=1)(k) SU(n(i)), which are obtained from decomposing the supersymmetry breaking model of Affleck, Dine and Seiberg containing an antisymmetric tensor field. We note that all of these models are distinct vacua of a single SU(N) gauge theory with an adjoint superfield. The dynamics of this model may be analyzed using the duality of Kutasov and Schwimmer and the deconfinement trick of Berkooz. This analysis leads to a simple picture for supersymmetry breaking for k = 2, complementing that of previous work. We examine the flat directions of these models, and give straightforward criteria for lifting them, explaining the requisite peculiar form of the superpotential, For all cases with k > 2, the duality argument fails to give supersymmetry breaking dynamics, and we identify a class of problematic flat directions, which we term 2m-baryons. We study in some detail the requirements for lifting these directions, and uncover some surprising facts regarding the relationship between R-symmetry and supersymmetry breaking in models with several gauge groups. (C) 1997 Elsevier Science B.V.