hereon UK /hɪəɹˈɒn/US /hɪɹˈɑn/ adverb4 •On this place.To the right of the brink of the precipice, and far over it, projects a narrow ledge. The test of legitimacy in the Ohonoo monarchs is to stand hereon, arms folded, and javelins darting by. — 1849 •To this place. •On this subject or basis. •Hereupon.