In this Paper we consider the supersymmetric (SUSY) FRW models interac
ting with the simplest real scalar matter supermultiplet. For these mo
dels we obtain potentials, which allow spontaneous breaking of SUSY. T
his happens for k = 0 and k = 1 when the energy density of the vacuum
of the scalar field is zero and also for k = 1 when this energy densit
y is similar to m(3/2)(2)M(p)(2).