We revisit and generalize, to the Einstein–Yang–Mills–Higgs (EYMH) system, previous
results of Christodoulou and Chae concerning global solutions for the Einstein-scalar field
and the Einstein–Maxwell–Higgs (EMH) equations. The novelty of the present work is
twofold. For one thing, the assumption on the self-interaction potential is improved. For
another thing, explanation is furnished why the solutions obtained here and those proved
by Chae for the EMH system decay more slowly than those established by Christodoulou
in the case of self-gravitating scalar fields. Actually, this latter phenomenon stems from
the non-vanishing local charge in EMH and EYMH models.