Arthur B. Haynes, a D.C. high school teacher, never has held public office or even chaired a civic association, but he thinks he can be elected executive of Prince George's County.

So do Kenneth W. Cutlip, a county police officer who couldn't get the endorsement of his own union, and John Lee Ball, a transient whose prime form of transporation around the sprawling county is walking.

Call them the Other Democrats, hardy individuals unaligned with the county's dominant Democratic clique who have spent the summer trudging from forum to debate to reception, passing out literature and generally struggling for notice in their battle to become the Democratic nominee for the top job in county government.

By almost any traditional barometer -- money, organization, name recognition or grass-roots support -- they are good bets to lose the nommination to councilman Parris Glendening. They nonetheless are confident. Their chief resources are a few new ideas and a faith untempered by conventional political wisdom.

Haynes' organization consists of himself and a few friends; his $1,800 campaign war chest comes mostly from what he was saving to fix his 8-year-old station wagon and buy his fall and winter wardrobe.

Haynes says, "my candidacy is a serious matter . . . in spite of all the odds I don't think you'll find anybody who is out there who's seen me campaign who would doubt that I'm serious."

"No question it's going to be tough," said Cutlip, who has raised about $2,500. Even though his own union, the Fraternal Order of Police, endorsed Glendening, Cutlip said, "I'd say I have a 50-50 chance right now."

Cutlip and Haynes acknowledge that the man to beat is Glendening, a two-term council member and Ph.D budget expert who teaches political science at the University of Maryland.

Glendening, a member of the county's dominant Democratic faction, began plotting his campaign well over a year ago. That was before political insiders knew whether the incumbent county executive, Republican Lawrence Hogan, would seek reelection to the office he won by a landslide in 1978. Hogan's subsequent decision to run for the U.S. Senate left the methodical but uncharismatic Glendening with nearly every endorsement considered worth having. He has raised more than $150,000, opened two offices and invested in expensive radio advertising.

Such is Glendening's sense of well being that he held a victory party at one of his campaign offices on the eve of the July 16 deadline for filing candidacy papers. He recently answered a question about his opponents' chances by pointing up at a warm August sky and declaring, "Is that a snowflake? I think I see a better chance for a blizzard tonight."

Such derision does not deter Haynes, Cutlip, or even Ball, who also ran against former county executive Winfield Kelly in 1978. Of the four primary challengers, Ball has adopted the most relaxed approach. Neither he nor his treasurer has a listed telephone number, and repeated attempts to contact him for an interview failed. Ball was spotted at one political function, a television debate taped Aug. 1. Yet Ball is not lacking in determination: He walked the 12 miles to the television studio for the taping.

Haynes, 47, and Cutlip, 36, have made the regular rounds of candidates' nights and civic association meetings. Though their campaign platforms are similar, and, they admit, they have even come to like each other, their views on the proper direction of government differ sharply.

Haynes, a teacher at Anacostia Senior High School in Southeast Washington, sent a letter to newspaper editors before his June announcement pointing out that he is the first black candidate for executive under the county's 10-year-old system of charter government.

"If my goal were simply to remove the 'WHITE ONLY' sign from the race for county executive, I would have achieved my goal on . . . the date I filed my certificate of candidacy," he wrote. Haynes, who has lived in Capitol Heights since 1968, points to a background in education (he is an industrial arts teacher), civil rights (as a participant in numerous voter registration projects in his native Georgia), and labor (as a teachers' union representative) as proof that he is qualified for the job of the 3,400 employe government and its half-billion dollar budget.

If elected, Haynes said, he would consider educational funding a priority, and the schools would be funded at a flat rate of 62 percent of the annual county budget. He vows to establish better public transportation, especially to the county seat in Upper Marlboro, and says he wants to attract light industry to the county. He also vows to find ways to revitalize older inner Beltway homes, to preserve farm land and to create a government-sponsored farmer's market.

Haynes also wants to repeal the TRIM amendment, which limits the amount of property tax revenue the county can collect to the 1979 level. He attacks Glendening mainly for failing to campaign strongly enough against TRIM when it appeared on the ballot four years ago.

"Pretty much every politician dodged the issue," said Haynes, who ran unsuccessfully for an at-large seat on the County Council in 1978. "All of these people were in office, and they should have been responsible enough to say, 'We're going to be in trouble.' "

Cutlip, on the other hand, paints himself as the fiscal conservative candidate who defends TRIM, which passed by a 3-to-1 margin in 1978. He also says he represents "the true, average citizen out here," and is "the candidate of inexperience."

Cutlip is an eight-year veteran of the county police force currently assigned to the safety education division. He never has run for office before. His community involvement has centered on lobbying for tougher drunk driving legislation, recently serving on the county's drunk driving task force.

He believes the county schools can be fully funded without amending TRIM by "cutting waste," although beyond saying that administrative offices should be consolidated, he declined to cite specific areas. In answer to many of a reporter's questions in a recent interview, Cutlip preferred to hand out his package of press releases.

Among those documents were proposals to establish a "self-funded" county-wide day care system; reinstate corporal punishment in the schools, and establish a county-owned public transportation system akin to Montgomery County's Ride-On buses. Cutlip said he is "committed to erasing the ugly sister image that our county has acquired through the sleazy zoning decisions by our County Council resulting in haphazard zoning throughout the county and the stigma attached to Prince George's County through their unscrupulous actions while in office."

Cutlip said he really preferred not to run, but feels that the voters are ready to give him a chance. "If I'd found somebody who I liked for county executive I would have been all out. I don't like the limelight. But," he added emphatically, "There's been very controversial issues out here. People have seen what experience can do. I think they're ready to say, 'let's give inexperience a chance.' "