We study N=1 global and local supersymmetric theories with a continuousglobal $U(1)_R$ symmetry as models of dynamical supersymmetry (SUSY) breaking.We introduce explicit R-symmetry breaking terms into such models, in particulara generalized O'Raifeartaigh model. Such explicit R-symmetry breaking terms canlead to a SUSY preserving minimum. We classify explicit R-symmetry breakingterms by the structure of newly appeared SUSY stationary points as aconsequence of the R-breaking effect, which could make the SUSY breaking vacuummetastable. We show that the R-breaking terms are basically divided into twocategories. One of them does not generate a SUSY solution, or yields SUSYsolutions that disappear in the case of supergravity when we tune a parameterso that the original SUSY breaking minimum becomes a Minkowski vacuum. We alsoshow that the general argument by Nelson and Seiberg for a dynamical SUSYbreaking still holds with a local SUSY except for a certain nontrivial case,and present concrete examples of the exception.
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