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This study presents an analysis of the long‐term variations of four propagating quasi 16‐day waves with Wavenumbers 1 and 2 and investigates their association with sudden stratospheric warming (SSW) events. The study is based on the data obtained from Aura Microwave Limb Sounder satellite and Modern‐Era Retrospective Analysis for Research and Applications‐2 reanalysis data in the period from 2004 to 2018. Strong quasi 16‐day waves are found in the winter hemisphere. The propagating waves with Wavenumber 1 are prominent in the Northern Hemisphere and eastward‐propagating waves are dominant in the Southern Hemisphere. By analyzing 14 SSW events, we found that the westward‐propagating quasi 16‐day waves increase rapidly around the onset dates of the major SSWs, which is likely associated with the quickly reduced mean eastward background winds. Based on analysis of geopotential height, Ertel potential vorticity and Eliassen‐Palm flux, the propagating quasi 16‐day waves with Wavenumbers 1 and 2, (mainly from westward‐propagating components) contribute to the formation of the vortex displaced and vortex split SSWs, respectively. Key Points: The variations of the quasi 16‐day waves and their response to SSWs are revealed using an extensive datasetThe rapidly reduced eastward winds during major SSWs are associated with the enhancement of the westward‐propagating quasi 16‐day wavesThe quasi 16‐day waves with Wavenumbers 1 and 2 contribute the formation of the displaced vortex and the split vortex, respectively [ABSTRACT FROM AUTHOR]