  This contribution begins the study of the complete superfield Lagrangian
description of the interacting system of D=4 N=1 supergravity (SUGRA) and
supermembrane. Firstly, we review a 'three form supergravity' by Ovrut and
Waldram, which we prefer to call 'special minimal supergravity'. This off-shell
formulation of simple SUGRA is appropriate for our purposes as the
supermembrane action contains the so-called Wess-Zumino term given by the
integral over a three form potential in superspace, C3. We describe this
formulation in the frame of Wess--Zumino superfield approach, showing how the
basic variations of minimal SUGRA are restricted by the conditions of the
existence of a three-form potential C3 in its superspace. In this language the
effect of dynamical generation of cosmological constant, known to be
characteristic for this formulation of SUGRA, appears in its superfield form,
first described by Ogievetsky and Sokatchev in their formulation of SUGRA as a
theory of axial vector superfield. Secondly, we vary the supermembrane action
with respect to the special minimal SUGRA superfields (basic variations) and
obtain the supercurrent superfields as well as the supergravity superfield
equations with the supermembrane contributions.
