This chapter examines the dilemma of power system resonance stability analysis based on the impedance model. The first aspect of this dilemma is the “cutting the feet to fit the shoes” predicament. In this analogy, “cutting the feet” means discarding the higher-order harmonic components in nonlinear devices’ incremental response, which significantly reduces the accuracy of the derived LTI model. The second aspect is the “walking into a dead-end path” predicament—the unsuccessful attempt to analyze power system resonance stability using frequency-coupled impedance models. The chapter explores key topics: incremental linearization methods using Taylor and Fourier series expansions at DC operating points; total-quantity harmonic linearization using Fourier series expansion; incremental harmonic linearization using Taylor and Fourier series expansions at AC steady-state operating points; properties of the frequency-coupled impedance model; and why this model proves unsuitable for resonance stability analysis.