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We develop analytic methodologies for stability analyses (using nonlinear and linear methodologies) of parallel dc-dc converters (under unsaturated and saturated operating conditions) using their switching model, discrete model (based on nonlinear map), and averaged model. We describe the approach for investigating the behavior of the stable and unstable equilibrium solutions of a parallel dc-dc converter under parametric variations and illustrate the methodology using a load-sharing dc-dc buck converter. For unsaturated operating condition, using bifurcation analysis and Floquet theory, we predict the stability boundary of the nominal solution, determine its postinstability dynamics, and investigate the dependence of the converter dynamics on its initial conditions. Subsequently, we demonstrate the differences in the predictions of the instabilities and instability boundaries using (conventional) linearized averaged (small-signal) and discrete and switching models.