  We study spontaneous supersymmetry breaking in inhomogeneous extensions of
${\cal N}=1$ supersymmetric field theory models in 4-dimensions. The ${\cal
N}=1$ Abelian Higgs model with the inhomogeneous mass parameter and the FI
coefficient that are dependent on spatial coordinates, as well as the
O'Raifeartaigh model with all its parameters being dependent on spatial
coordinates, are studied in detail. In the presence of inhomogeneous
parameters, half supersymmetry can be preserved by adding appropriate
inhomogeneous deformations to the original Lagrangians. The inhomogeneous
deformations often break the R-symmetry explicitly. In cases where the
inhomogeneous deformations do not break the R-symmetry explicitly, we
demonstrate that spontaneous breaking of the R-symmetry is infeasible. We argue
that those models can not be spontaneous supersymmetry breaking models,
according to the Nelson-Seiberg argument. We comment on this issue in the
context of a generic ${\cal N}=1$ supersymmetric model as well.
