We examine the infra-red structure of soft supersymmetry breaking masses ofthe squarks and sleptons in supersymmetric (SUSY) strong unification schemeswhere $\alpha_{GUT}\sim 0.2-1$. We show that combinations of soft massesapproach fixed points which leads to very simple predictions for soft masses atthe intermediate scale. The assumption that the high energy gaugino mass$M_{1/2}$ dominates over the soft scalar masses leads to a strong suppressionof flavour changing neutral currents, and a low energy SUSY spectrum which issimply predicted in terms of two parameters, namely $\alpha_{GUT}$ and$M_{1/2}$. Due to the quickly falling gauge couplings beneath the high energyscale, the low energy spectrum has a characteristic ``scalar dominated''signature quite unlike the standard gaugino dominated MSSM where theright-handed sleptons are predicted to be rather light. We also examine the newsources of flavour changing expected in such models, and in particular showthat the flavour violation coming from the D-term of a $U(1)_X$ gauged familysymmetry may be reduced to an acceptable level.
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