The　health　monitoring　and　diagnosis　of　rotating　machinery　under　nonstationary　conditions　are　still　challenging　due　to　the　complex　modulation　characteristics　and　the　interfering　noises.　In　this　paper,　a　novel　flexible　iterative　generalized　demodulation　filtering　method　is　proposed　for　the　machinery　fault　diagnosis.　First,　the　Hilbert　transform　is　applied　to　the　vibration　signals　to　highlight　the　characteristic　frequencies　as　well　as　their　harmonics.　Second,　the　phase　functions　used　for　mapping　the　interest　frequencies　are　designed,　and　no　matter　how　the　speed　varies,　the　time-varying　frequencies　of　different　signal　segments　with　the　same　physical　meaning　are　transformed　into　the　same　constant　frequencies.　Then,　the　filters　are　designed　based　on　the　introduced　base　frequency　and　the　characteristic　coefficients,　and　then　the　modulation　rotating　frequency,　fault　characteristic　frequencies,　and　their　harmonics　are　filtered.　Finally,　the　demodulated　signals　are　reconstructed　and　the　health　conditions　are　determined　by　the　demodulated　spectrums.　The　method　is　evaluated　by　the　vibration　signals　of　faulty　rolling　bearings　and　planetary　gearboxes.　The　results　demonstrate　that　the　method　can　well　reveal　the　fault-related　frequencies　and　that　the　demodulated　frequency　values　are　not　subject　to　the　speed　fluctuation　profiles.