nonterritorial has no recorded synonym. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. Its one recorded opposite is territorial.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
not displaying territoriality
“a nonterritorial species”
Synonyms, antonyms and the broader and narrower relations for nonterritorial come from Princeton University’s WordNet. Full sources and licences.