  Gauge-Yukawa unified theories, and in particular those which are finite
beyond the unification scale, have been extended to include a soft
supersymmetry breaking (SSB) sector. In the case of the Finite Unified Theories
a new solution to the condition of two-loop finiteness of the SSB parameters is
found, which requires a sum rule for the relevant scalar masses. The sum rule
permits violations of the universality of the scalar masses which is found to
lead to phenomenological problems. The minimal supersymmetric SU(5)
Gauge-Yukawa model and two Finite-Gauge-Yukawa models have been examined using
the sum rule. The characteristic features of these models are: a) the old
agreement of the top quark mass prediction persists using the new data, b) the
lightest Higgs boson is predicted to be around 120 GeV, c) the s-spectrum
starts above 200 GeV.
