  The plethora of scalar fields participating in the formulation of a softly
broken supersymmetric theory can threat the stability of the standard vacuum.
The generic situation is twofold. Directions in scalar field space may exist
along which the potential becomes unbounded from below or local minima deeper
than the standard one are likely to appear where charge and/or color symmetries
are broken. An investigation of these matters requires a thorough study of the
tree level effective potential as well as its radiative corrections. However,
the presence of many different mass scales in such a generic supersymmetric
theory needs an appropriate renormalization improved treatment. Combining the
decoupling theorem with a conveniently chosen renormalization scale for each
field configuration, the well known multimass scale problem is circumvented. In
this context, the ordinary universal soft-parameters case of the minimal
supersymmetric model as well as a non-universal case of a brane world minimal
supergravity model are examined closely for unphysical vacuua.
