Performance analysis of modern communication systems has lead to a revision and sharpening of nonlinear stability analysis techniques developed over the last century. Applicability of such techniques involves a number of areas, including: process control systems, active queue management in data networks, and other branches of engineering. This monograph presents some recent performance analysis results within a unified stability analysis framework. Several interesting counterexamples to the existing nonlinear stability theory are given. Additionally, several cutting-edge case studies from air traffic control systems and data networks are presented to further illustrate the applications of the theory. The main theoretical results build upon the well-established multiplier theory, which has received much interest because of recent advances in software packages such as the linear matrix inequality (LMI) toolbox. The exposition demonstrates the existence of monotone nonlinearites in problems of interest and gives an exhaustive stability analysis treatment of systems containing such nonlinearities. Key features: * broad range of topics: stability analysis, monotone nonlinearities, multiplier theory, service quality in data networks, protocol scalability, air traffic congestion control * recent and original results presented * many examples and case studies illustrate the applicability of the theory * comprehensive glossaries, bibliography, index, and appendices "Qualitative Nonlinear Dynamics of Communication Networks" is a useful reference for graduate students, and practitioners in control, computer, electrical, aerospace, and mechanical engineering. It can be used as a supplementary textfor nonlinear stability courses at the graduate level. Prerequisites are a familiarity with elementary control theory, linear systems theory, matrix theory, and functional analysis.