We analyze the structure of the vacuum and supersymmetry breaking patt
ern in Fayet-Iliopoulos models with dynamical gauge coupling and Planc
k-scale value of the FI parameter. We show that in this class of model
s supersymmetry is generically broken, but the mere presence of the D-
term is not sufficient to stop the running away of the modulus respons
ible for the value of the gauge coupling - the dilaton. To stabilize t
he dilaton, one has to include an additional dilaton-dependent part in
the superpotential. The presence of a large D-term gives rise to the
mixed dilaton/D-term dominated scenarios of susy breaking, which allow
horizontal hierarchy generation. Models that can serve as secluded se
ctors in gauge mediation scenarios are discussed. It is shown that whe
n the FI parameter and the gauge coupling are dynamical variables, the
D-term dominated Universe does not allow for an inflationary period.
(C) 1998 Elsevier Science B.V.