The formalism of graded Poisson-sigma models allows the construction of
N=(2,2) dilaton supergravity in terms of a minimal number of fields. For the
gauged chiral U(1) symmetry the full action, involving all fermionic
contributions, is derived. The twisted chiral case follows by simple
redefinition of fields. The equivalence of our approach to the standard second
order one in terms of superfields is presented, although for the latter so far
only the bosonic part of the action seems to have been available in the
literature. It is shown how ungauged models can be obtained in a systematic way
and some relations to relevant literature in superstring theory are discussed.Comment: 26 p., LaTeX. v3: extended version, new title, new section on
ungauged model
