Our purpose is to attempt to apply the probabilistic methods of Markov chains to a systematic study of the phenomena of brand switching and brand loyalty. After summarizing the traditional basic concepts of Markov chains, we introduce concepts from the theory of directed graphs in order to provide a geometric and intuitive point of view. We then demonstrate that the set of all brands of a particular product category can be validly regarded as a concrete case of an abstract Markov chain. The implications of this approach for marketing strategy are also indicated. A simplified situation is employed to indicate various applications. This is followed by a discussion of real applications.