  The supersymmetric generalization of dilatations in the presence of the
dilaton is defined. This is done by defining the supersymmetric dilaton
geometry which is motivated by the supersymmetric volume preserving
diffeomorphisms. The resulting model is classical superconformal field theory
with an additional dilaton-axion supermultiplet coupled to the supersymmetric
gauge theory, where the dilaton-axion couplings are nonrenormalizable. The
possibility of spontaneous scale symmetry breaking is investigated in this
context. There are three different types of vacua with broken scale symmetry
depending on the details of the dilaton sector: unbroken supersymmetry,
spontaneously broken supersymmetry and softly broken supersymmetry. If the
scale symmetry is broken in the bosonic vacuum, then the Poincar\'e
supersymmetry must be broken at the same time. If the scale symmetry is broken
in the fermionic vacuum but the bosonic vacuum remains invariant, then the
Poincar\'e supersymmetry can be preserved as long as the R-symmetry breaking is
specifically related to the scale symmetry breaking.
