running battle noun2 •A fight that moves, with attacks occurring in various places.A ferocious running battle now developed between the Heinkels and their escort and the Spitfires and Hurricanes of 72, 605, 41 and 79 Squadrons. — 2010 •A conflict that continues over a long period of time, usually with periodic eruptions of fighting.Not only did they not get on, but they also had a constant running battle which had become increasingly bitter over time. — 2007 formsrunning battles