  Requiring the soft supersymmetry-breaking (SSB) parameters in finite
gauge-Yukawa unified models to be finite up to and including two-loop order, we
derive a two-loop sum rule for the soft scalar-masses. It is shown that this
sum rule coincides with that of a certain class of string models in which the
massive string states are organized into N=4 supermultiplets. We investigate
the SSB sector of two finite SU(5) models. Using the sum rule which allows the
non-universality of the SSB terms and requiring that the lightest superparticle
particleis neutral, we constrain the parameter space of the SSB sector in each
model.
