To have a disagreement or dispute; to get into a conflict or quarrel, often over an issue or negotiation.
彼らは遺産をめぐってもめている。
They are disputing over the inheritance.
会議で意見が食い違ってもめた。
A disagreement occurred in the meeting because opinions clashed.
近所で騒音をめぐってよくもめることがある。
There are often disputes in the neighborhood over noise.