The doctoral thesis is devoted to the investigation of nonlinear dynamics of switching power converters on the basis of Method of Complete Bifurcation Groups, applying the obtained results to solve the converter stability ensuring and electromagnetic noise suppression problems. Within the thesis the complex dynamics of buck and boost converters, operating in continuous and discontinuous conduction modes, has been studied, revealing typical bifurcation sequences and chaotization scenarios. Main instruments used to investigate nonlinear dynamics of switching converters are analytical stability estimation methods of periodic regimes, discrete-time and averaged models of converters, simulations within PSpice and SIMULINK and laboratory experiments. The results of thesis and developed algorithms could be applied to design of stable and qualitative switching power converters. The doctoral thesis includes 263 pp., 117 figures, 8 tables, 7 appendices and 198 sources of literature.