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The convergence behavior of an adaptive processor is usually a very important aspect of the system's performance and in fact many processor parameters are usually chosen with the goal of optimizing, or at least manipulating, the convergence rate. In spite of this common interest, several methodologies for analyzing convergence behavior have been developed, principally because different applications often require different behavioral knowledge and because no single technique provides all the answers. The purpose of this paper is to compare and contrast convergence analysis techniques used in the fields of adaptive filtering, adaptive identification, and adaptive control. The methods explored include both nonlinear stability analysis and stochastic analysis. Particular attention is paid to the underlying assumptions and useful outputs for each approach.