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This position paper advocates the use of the well de- fined and provable self-stabilization property of a sys- tem, to achieve the goals of the self-* paradigms and au- tonomic computing. Several recent results starting from hardware concerns, continuing with the operating sys- tem, and ending in the applications, are integrated: the self-stabilizing microprocessor, with the self-stabilizing operating system, the self-stabilization preserving com- piler, and the self-stabilizing autonomic recoverer for applications.