Synonyms of 'on the move'
▷ See move
1 in transitDictionary, moving, travellingMy husband and I were always on the move.
2 activeDictionary, moving, developingAviation is on the move, and many airlines are forming alliances.
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Thesaurus for on the move from the Collins English Thesaurus
If you are on the move , you are going from one place to another.