TheYang-Mills-HiggsfieldgeneralizestheYang-Millsfield.TheauthorsestablishthelocalexistenceanduniquenessoftheweaksolutiontotheheatflowfortheYang-Mills-HiggsfieldinavectorbundleoveracompactRiemannian4-manifold,andshowthattheweaksolutionisgauge-equivalenttoasmoothsolutionandthereareatmostfinitesingularitiesatthemaximumexistingtime.