Howard County Executive Edward L. Cochran, 49, was defeated in Tuesday's Democratic primary by J. Hugh Nichols, a former member of the House of Delegates who has a reputation as a budget expert.

Nichols, 47, of Columbia finished with 9,317 votes, or 57 percent, against 6,083 votes, or 37 percent, for Cochran. Ellicott City's C. Howard Strahler was a distant third with 848 votes.

Nichols, a former assistand secretary in the Maryland Budget Department, will face Republican James Ansell in the general election.

State Sen. James Clark Jr., a political ally of Nichols, said that budget control and efficient government were key issues in the county executive's campaign.

All five Democratic incumbents on the HOward County Council were renominated from a field of 10. Winning renomination were Elizabeth Bobo (9,287 votes); Ruth Keeton (8,501); Lloyd G. Knowles (8,019); Virginia Thomas (7,772) and Thomas M. Yeager (6,648).

They will face Republican nominees Robert H. Kittleman (2,609); J. Michael Marshall (2,280); Charles E. Miller (2,458); L. Trent Mitchell (2,538) and William M. Maratein (2,011).

William R. Hymes, 51, a former assistant state's attorney from Ellicott City, unseated incumbent State's Attorney Charles E. Wehland, 8,093 to 6,455. Hymes will face independent Timothy Welsh in the general election.

Incumbent Democratic Sheriff John H. Votta was renominated with 58 percent of the vote in a field of four and will face Republican Wilson Gamber Sr. in the general election.

Barbara L. Russell, a member of the Board of Education, won reelection in a field of three. She has no general election opponent. ANNE ARUNDEL COUNTY

Republican County Executive Robert A. Pascal, who resisted entreatiest to run for governor, was easily renominated for the county executive's seat. He piled up 9,164 votes over challenger Daniel J. Bedsole III, who had 2,034.

Pascal will face Democrat Elmer E. Dunn Sr. in the general election. Dunn captured 45 percent of the vote in a four-man Democratic primary to win.

Three Democratic incumbents were renominated in contested Anne Arundel County Council primaries. In District 3, Incumbent Sarah Evelyn Carter defeated George E. Mills, 15,158 to 13,396. She will face Republican Francis Jones in the general election.

In District 5, incumbent Edward C. Ahern Jr. was renominated by defeating Ernest C. Kopp and Thomas H. Venture. Ahern's general election opponent is Republican John G. Gary Jr.

In District 7, incumbent Virginia P. Clagett defeated Charles T. Brewer and William R. Thompaon. She will oppose Republican Mary Sellman Jackson in the general election.

There was no incumbent running in District 6. William Brill captured the Democratic nomination in a field of four and will face Don C. Hall II in the general election.

First District Councilman George F. Bachman Jr. is unopposed in the general election. In District 2, Democratic incumbent Ronald C. McGuirk will face Republican Gary Lynn Martin. In District 4, incumbent Democrat Wallace R. Childs will face Republican Diane R. Evans.

Anne Arundel County Sheriff William R. Huggins was overwhelmingly reelected in a field of three. He has no general election opponent.