  We provide the geometric actions for most general N=1 supergravity in two
spacetime dimensions. Our construction implies an extension to arbitrary N.
This provides a supersymmetrization of any generalized dilaton gravity theory
or of any theory with an action being an (essentially) arbitrary function of
curvature and torsion.
  Technically we proceed as follows: The bosonic part of any of these theories
may be characterized by a generically nonlinear Poisson bracket on a
three-dimensional target space. In analogy to a given ordinary Lie algebra, we
derive all possible N=1 extensions of any of the given Poisson (or W-)
algebras. Using the concept of graded Poisson Sigma Models, any extension of
the algebra yields a possible supergravity extension of the original theory,
local Lorentz and super-diffeomorphism invariance follow by construction. Our
procedure automatically restricts the fermionic extension to the minimal one;
thus local supersymmetry is realized on-shell. By avoiding a superfield
approach we are also able to circumvent in this way the introduction of
constraints and their solution. For many well-known dilaton theories different
supergravity extensions are derived. In generic cases their field equations are
solved explicitly.
