  We discuss certain integrable quantum field theories in (1+1)-dimensions
consisting of coupled sine/sinh-Gordon theories with N=1 supersymmetry,
positive kinetic energy, and bosonic potentials which are bounded from below.
We show that theories of this type can be constructed as Toda models based on
the exceptional affine Lie superalgebra $D(2,1;\A)^{(1)}$ (or on related
algebras which can be obtained as various limits) provided one adopts
appropriate reality conditions for the fields. In particular, there is a
continuous family of such models in which the couplings and mass ratios all
depend on the parameter $\A$. The structure of these models is analyzed in some
detail at the classical level, including the construction of conserved currents
with spins up to 4. We then show that these currents generalize to the quantum
theory, thus demonstrating quantum-integrability of the models.
