- 1. Department of Physics, Ben-Gurion Univ. of the Negev, Beer-Sheva 84105, Israelguendel@bgu.ac.il , email@example.com. Institute of Nuclear Research and Nuclear Energy, Bulg. Acad. Sci., So a 1784, Bulgarianissimov@inrne.bas.bg , firstname.lastname@example.orgAbstractWe present a qualitatively new mechanism for dynamical spontaneous breakdown of supersymmetry.Speci cally, we construct a modi ed formulation of standard minimal N = 1 supergravity. The modi ca-tion is based on an idea worked out in detail in previous publications by some of us, where we proposed anew formulation of (non-supersymmetric) gravity theories employing an alternative volume form (volumeelement, or generally-covariant integration measure) in the pertinent Lagrangian action, de ned in termsof auxiliary (pure-gauge) elds instead of the standard Riemannian metric volume form. Invariance un-der supersymmetry of the new modi ed N = 1 supergravity action is preserved due to the addition ofan appropriate compensating antisymmetric tensor gauge eld. This new formalism naturally triggersthe appearance of a dynamically generated cosmological constant as an arbitrary integration constantwhich signi es a spontaneous (dynamical) breaking of supersymmetry. Furthermore, applying the sameformalism to anti-de Sitter supergravity allows us to appropriately choose the above mentioned arbitraryintegration constant so as to obtain simultaneously a very small e ective observable cosmological con-stant as well as a large gravitino mass as required by modern cosmological scenarios for slowly expandinguniverse of today.