BOSTON — Affirmative action policies at Harvard University and the University of North Carolina at Chapel Hill have been challenged in court.

A lawsuit against Harvard alleges the university limits the number of Asian-Americans it admits each year, arguing that white, black, and Hispanic applicants are given racial preferences over better qualified Asian-American applicants.

The lawsuit against UNC alleges the university is not in compliance with a Supreme Court ruling that concluded colleges trying to diversify their student population should pursue “race-neutral alternatives” first, rather than race-based affirmative action policies.

The suits were filed Monday in Boston and Greensboro, North Carolina, by the Project on Fair Representation.

The plaintiff in both is Students for Fair Admissions, a nonprofit whose members include students and parents.

The universities didn’t respond to requests for comment.

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