We constrain the parameter space of the minimal and gaugino-assisted anomaly mediation, and gaugino mediation models by requiring that the electroweak vacuum corresponds to the deepest minimum of the scalar potential. In the framework of anomaly mediation models we find strong lower bounds on slepton and squark masses. In the gaugino mediation models the mass spectrum is forced to be at the TeV scale. We find extensive regions of the parameter space which are ruled out, even at low tanbeta. The implications of these results on the g-2 of the muon are also analyzed.
