Numerous　mechanical　nonstationary　fault　signals　are　a　mixture　of　sustained　oscillations　and　nonoscillatory　transients,　which　are　difficult　to　efficiently　analyze　using　linear　methods.　We　propose　a　nonlinear　demodulation　analysis　method　based　on　resonance　and　apply　it　to　the　fault　diagnosis　of　rolling　bearings.　Unlike　conventional　demodulation　methods　that　use　frequency-based　analysis　and　filtering　techniques,　our　nonlinear　demodulation　analysis　method　is　a　decomposition　demodulation　of　the　signals　according　to　different　resonance　based　on　Q-factors.　When　a　local　rolling　bearing　fault　such　as　pitting　is　present,　the　fault　vibration　signals　consist　of　the　regular　vibration　signals　and　noise　(a　high　resonance　component　containing　multiple　simultaneous　sustained　oscillations)　and　a　transient　impulse　signal　(a　low　resonance　component　being　a　signal　containing　nonoscillatory　transients　of　faults).　The　regular　vibration　signal　is　a　narrowband　signal　that　has　a　high　Q-factor,　and　the　transient　impulse　signal　is　a　wideband　signal　that　has　a　low　Q-factor.　Using　our　resonance-based　nonlinear　demodulation　analysis　method,　we　decompose　the　signal　into　high　resonance,　low　resonance,　and　residual　components.　Then,　we　perform　a　demodulation　analysis　on　the　low　resonance　component　that　includes　the　fault　information.　We　have　verified　the　feasibility　and　validity　of　the　algorithm　by　analyzing　the　results　of　experimental　and　engineering　signals.