We examine in a cosmological context the conditions for unbroken supersymme
try in N=1 supergravity in D=10 dimensions. We show that the cosmological s
olutions of the equations of motion obtained considering only the bosonic s
ector correspond to vacuum states with spontaneous supersymmetry breaking.
With a nonvanishing gravitino-dilatino condensate we find a solution of the
equations of motion that satisfies necessary conditions for unbroken super
symmetry and that smoothly interpolates between Minkowski space and de Sitt
er space with a linearly growing dilaton, thus providing a possible example
of a supersymmetric and nonsingular pre-big-bang cosmology. [S0556-2821(99
)01402-2].