Volokh on Republic v. Democracy:

Eugene Volokh has an outstanding post that argues, correctly I might add, that the concepts of "republic" and "democracy" are not mutually exclusive. The United States, as founded, is aptly termed both a republic AND a democracy. It is not a "direct" or a "pure" democracy, rather a representative-democracy. Terms like that, representative-republic, democratic-republic, are six and one half dozen of the other.