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Regular Baptists are "a moderately Calvinistic Baptist denomination that is found chiefly in the southern U.S., represents the original English Baptists before the division into Particular and General Baptists, and observes closed communion and foot washing", according to Merriam Webster. This definition describes Old Regular Baptists, not those who formed as a result of the Fundamentalist-Modernist controversy.
The most prominent Regular Baptist group is the General Association of Regular Baptist Churches. While the term Regular Baptist was originally a reference to the Particular Baptists, it came to be used more loosely as a synonym for orthodox. The Baptist Bulletin of the GARBC defines them simply as groups who believe "orthodox, Baptist doctrine" and "affirm the rule or measure of the Scripture."