Relating to or characteristic of a city council or a member of a city council, especially in terms of their concerns or activities.
From council plus -manic (relating to mania or obsession, but here simply a suffix meaning 'of or relating to'), common in American municipal vocabulary.
Councilmanic is primarily an American English term—you'll see it used in newspapers like 'councilmanic affairs' or 'councilmanic districts,' and it often carries a slightly humorous or critical tone about local politics!
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