  We address a supersymmetric embedding of domain walls with asymptotically
anti-deSitter (AdS) space-times in five-dimensional simple, N=2 U(1) gauged
supergravity theory constructed by Gunaydin, Townsend and Sierra. These
conformally flat solutions interpolate between supersymmetric AdS vacua,
satisfy the Killing spinor (first order) differential equations, and the
four-dimensional world on the domain wall is a flat world with N=1
supersymmetry. Regular solutions in this class have the energy density related
to the cosmological constants of the supersymmetric AdS vacua. An analysis of
such solutions is given for the example of one (real, neutral) vector
supermultiplet with the most general form of the prepotential. There are at
most two supersymmetric AdS vacua that are in general separated by a
singularity in the potential. Nevertheless the supersymmetric domain wall
solution exists with the scalar field interpolating continuously across the
singular region.
