We consider the stability of non-supersymmetric critical points of generalN=4 supergravities. A powerful method to analyse this issue based on thesGoldstino direction has been developed for minimal supergravity. We adapt thisto the present case, and address the conceptually new features arising forextended supersymmetry. As an application, we investigate the stability whensupersymmetry breaking proceeds via either the gravity or the matter sector.Finally, we outline the N=8 case.
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