Nonaldermanic

As nonaldermanic members were, naturally, less informed concerning the problems with which the commission was concerned than were the aldermanic members, the chairman called a number of "seminar meetings" for the nonaldermanic members alone.

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A mayor of a nonaldermanic city or village does not have a veto power; a mayor in an aldermanic structure has very restricted voting powers;

Source: wiktionary

[…] evidence of nonaldermanic elections involving black candidates was admissible in § 2 vote dilution action as proof of local voting patterns, where district court had statistical data of only two city aldermanic elections.

Source: wiktionary

[…] there were still living in the City and Liberties fifteen nobleman and their ladies, one ambassador, and thirty-four nonaldermanic knights, some of them government contractors and officials like Sir Henry Spiller or Sir William Russell, some of them royal officials like Sir Robert Heath , others mere landed gentry like Sir Thomas Richardson.

Source: wiktionary