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The concept of multitolerance abstracts problems in system dependability and provides a basis for improved design of dependable systems. In the abstraction, each source of undependability in the system is represented as a class of faults, and the corresponding ability of the system to deal with that undependability source is represented as a type of tolerance. Multitolerance thus refers to the ability of the system to tolerate multiple fault-classes, each in a possibly different way. In this paper, we present a component based method for designing multitolerance. Two types of components are employed by the method, namely detectors and correctors. A theory of detectors, correctors, and their interference-free composition with intolerant programs is developed, that enables stepwise addition of components to provide tolerance to a new fault-class while preserving the tolerances to the previously added fault-classes. We illustrate the method by designing a fully distributed multitolerant program for a token ring.