Geometrical constraints and equations of motion in extended supergravity

Consequences of geometrical constraints from integrability along all super lightlike lines are examined in N-extended supergravity theories. It is shown that these constraints give rise, through Bianchi identities, to equations of motion of the conformal type for all forms of physical fields, with N>4. Our results point to an integrability program for N>4 supergravity similar to that for N>2 supersymmetric Yang-Mills fields.