Rotating　machinery　fault　diagnosis　under　nonstationary　conditions　still　mainly　relies　on　manual　analysis　of　the　frequency　spectrums　or　the　time-frequency　representations　of　vibration　signals.　However,　not　only　do　the　results　of　those　methods　depend　on　heavily　the　expert　experience,　but　for　some　samples,　the　intricate　interference　frequency　components　caused　by　the　complex　modulation　characteristics　and　the　operation　conditions　also　make　it　difficult　to　identify　the　frequency　content.　In　this　article,　a　novel　intelligent　fault　diagnosis　method　for　rolling　bearings　under　nonstationary　conditions　is　investigated.　A　new　flexible　generalized　demodulation　method　is　first　proposed.　Different　from　traditional　demodulation　methods,　it　can　map　the　interest　time-varying　frequencies　of　extensive　samples　under　different　speed　conditions　to　the　defined　base　frequency　as　well　as　its　multiples,　and　thus　overcomes　the　effects　of　operation　conditions　on　demodulation　spectrums.　Based　on　the　demodulation　method,　a　fault　feature　extraction　method　is　further　proposed　to　capture　the　useful　fault　information　in　the　spectrums.　Experiments　validate　that,　for　some　samples,　the　health　conditions　cannot　be　manually　identified　by　the　demodulation　spectrums　due　to　the　interference　frequency　components,　but　can　be　recognized　by　the　proposed　method　automatically,　and　because　of　the　definite　physical　meaning,　the　method　is　more　adaptive　to　new　operation　conditions.