Motion　estimation　in　videos　primarily　concerns　global　and　local　motion,　derived　from　different　subjects　but　mixed　in　video　frames.　In　fact,　in　most　scenes,　such　as　action　recognition,　it　is　necessary　to　estimate　the　global　and　local　motion　respectively　in　order　to　obtain　accurate　motion　representation.　Due　to　the　lack　of　ground-Truth　labels,　estimating　global　and　local　motion　simultaneously　poses　a　challenge.　In　this　work,　we　address　these　issues　with　an　end-To-end　two-stream　network　for　global　and　local　motion　estimation.　This　network　utilizes　the　mixed　motion　as　supervision,　employs　the　attention　mechanism　based　on　the　Transformer,　and　adopts　a　two-stage　training　strategy　for　mutual　enhancement　of　the　two　motions　during　training.　Additionally,　we　introduce　a　motion-based　feature　decoder　for　the　global　stream　and　a　SIR　mask　to　remove　scene-irrelevant　regions　for　the　local　stream.　We　verify　the　effectiveness　of　our　method　on　the　deep　homography　estimation　dataset　DHE,　action　recognition　dataset　NCAA,　and　group　activity　recognition　dataset　UCF-101.　Results　demonstrate　improved　performance　over　previous　methods　in　regular　scenes　and　recognition　tasks.　©　2023　IEEE.