  In the context of extended t-J models, with intersite Coulomb interactions,
nodal liquids are discussed. We use the spin-charge separation ansatz as
applied to the nodes of a d-wave superconducting gap. Such a situation may be
of relevance to the physics of high-temperature superconductivity. We point out
the possibility that at certain points of the parameter space supersymmetric
points may occur, characterized by dynamical supersymmetries between the spinon
and holon degrees of freedom, which are quite different from the symmetries in
conventional supersymmetric t-J models. Such symmetries pertain to the
continuum effective field theory of the nodal liquid, and one's hope is that
the ancestor lattice model may differ from the continuum theory only by
renormalization-group irrelevant operators in the infrared. We give plausible
arguments that nodal liquids at such supersymmetric points are characterized by
superconductivity of Kosterlitz-Thouless type.
