President Reagan has nominated local lawyers George W. Mitchell and Steffen W. Graae to 15-year terms as judges on the D.C. Superior Court.

Mitchell, 47, received his undergraduate and law degrees from Howard University and worked in the solicitor's office in the U.S. Department of Labor from 1960 to 1962.

He has had his own practice in Washington for 20 years, appearing regularly in Superior Court. He has been chairman of the D.C. Bar disciplinary committee and president of the Howard Law Alumni Association of Washington.

Graae, 41, and his partner, Lawrence H. Mirel, have been in private practice here since 1974.

Graae was born in Copenhagen, but is a U.S. citizen. He received an undergraduate degree from Yale University, a master's degree in politics and economics from Oxford University and graduated from Georgetown University Law Center in 1973. He served as a law clerk to U.S. District Court Judge John G. Penn while Penn was on the D.C. Superior Court.

Before entering law school, Graae held several positions in government agencies, including the Agency for International Development and the Office of Economic Opportunity. He was a consultant to the National Commission on the Causes and Prevention of Violence and has taught at Georgetown University.

Friday's nominations, if confirmed by the Senate, will mean that Reagan has named eight of the lower court's 44 judges. At least two more vacancies are expected this year. Judge Samuel B. Block is retiring in June and Judge Margaret A. Haywood is retiring in October.

Mitchell and Graae would fill two vacancies created when Judges William E. Stewart and Dyer Justice Taylor retired in February.