GeneSyS is an IST project (IST-2001-34162) developing a new generic middleware for supervising distributed systems at different levels such as Application, Network, System. The prototype implementation is based on Web technologies like Web Services, XML, and XML schema. This article presents the GeneSyS framework including support for intelligent supervision as well as results on applying GeneSyS for Web Servers monitoring. Since the developed framework is flexible and portable, the applicability to other contexts (HLA-compliant real-time simulators and business oriented Grid architectures) is shortly elaborated at the end of this article. KEYWORDS GeneSyS, Distributed Management, XML, Web Services, Intelligent Agent, Grid.