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.

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