  A t-J-like model for inhomogeneous superconductivity of cuprate oxides is
presented, in which local anisotropic magnetic terms are essential. We show
that this model predicts pairing, consistent with experiments, and argue how
the macroscopic phase-coherent state gradually grows upon lowering of the
temperature. We show that appropriate inhomogeneities are essential in order to
have significant pair binding in the thermodynamic limit. Particularly, {\it
local} breaking of SU(2) spin symmetry is an efficient mechanism for inducing
pairing of two holes, as well as explaining the magnetic scattering properties.
We also discuss the connection of the resulting inhomogeneity-induced
superconductivity to recent experimental evidence for a linear relation between
magnetic incommensurability and the superconducting transition temperature, as
a function of doping.
