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