1. To be literally marching or walking, as of an army. Enemy forces are on the march, and we expect them to arrive by morning.We've got to be on the march soon if we hope to reach the camp by sundown.
2. To be making progress or gaining momentum. Your new initiative is on the march—I heard the boss talking about it this morning!The new education bill is on the march—it looks like it will be approved without much resistance.