John F. Herrity, chairman of the Fairfax County Board of Supervisors, announced yesterday he will seek the Republican nomination for Congress to oppose Rep. Herbert E. Harris II, with whom he frequently feuded when both men were county supervisors in the early 1970s.

Herrity, a well-known Republican politician in Northern Virginia, began his campaign by accusing Harris, A Democrat, of "nonrepresentation" over the past four years in the Eighth Congressional District. The district comprises Alexandria, southern Fairfax County, all of Prince William County and part of Stafford County.

"During the course of this campaign I will be issuing a number of challenges to Mr. Harris to explain his record," Herrity said. He challenged Harris yesterday to explain why he voted for President Carter's proposed crude oil tax and failed to mention his vote to constituents in a newsletter about energy policy.

Herrity also accused Harris of turning last year's Northern Viginia water crisis into a "partisan political issue." At a hearing last month Harris, who is chairman of the House District subcommitte on regional affairs, directed much of the blame for the water shortage at Herrity.

Harris'press secretary, Jack Sweeney, said yesterday the congressmen has no comment on Herrity's announced candidacy or on of his charges."Rep. Harris still has a year of congressional work ahead of him," Sweeney said. 'It is too soon to start thinking about politics."

Some Fairfax politicians said, however, that Harris should be worried about Herrity, whose name is well known in the district. "The fact that they don't like each other could turn (the race) into a real donnybrook," one observer said.

Before Herrity can face off against Harris, he must win the Republican primary on June 13. In his press conference yesterday, Herrity said he had "the best chance of any Republican of beating Harris,"

Herrity's likely opponents in the Republican primary are Robert L. Thoburn and Robert E. Harris, both Fairfac County delegates to the General Assembly.

Thoburn, a fundamentalist minister from Fairfax who describes himself as a "consistent conservative," said yesterday he plans to announce his candidacy in March, Thoburn said he plans to run against Harris and against big government, and that he plans to stick to his strongly conservative positions throughout the campaign against Herrity. "I don't care if it is good politics or not," he said. Del. Harris, who is often confused with Rep. Harris, said yesterday, he too plans to announce his candidacy on March, and also was prepared to comment on Herrity't candidacy.

"I'm concerned as many citizens are about the condition of Herrity's health," Harris said. Herrity's suffered two heart attacks shortly after taking office as chairman of the Board of Supervisors in 1976.

"Basically a third of his (Herrity's) heart is dead," Harris said. "With the stress of a campaign I wonder if he is properly advised to jump into a campaign."

Herrity, 46, who lost weight and now runs 3 1/2 miles every morning, responded to Robert Harris' remarks yesterday by challenging him to footrace. Herrity, in his press conference, also challenged Rep. Harris to a foot race "from Pennslylvania Avenue to Capitol Hill" and said his doctor recently told him he is in better health than "99 percent of the people his age in the country."

At his press conference yesterday, Herrity said he is concerned that "unilateral intervention" by the federal governmentinto local government and lives of individuals has gone too far. As a supervisor he has consistently criticized federal laws that force higher taxes on the county.

One of Herrity's main targets of criticism in the past decade has been Metro, and he said yesterday that "something has to be done about the bus system in Northern Virginia." He cited declining patronage, declining service and increased fares, and said Northern Viginia governments should "look into" operating their own systems.