The last time the brothers of Kappa Alpha Psi wanted to hold their national convention in Washington, none of the major hotels in town would host them. Instead, the black fraternity met at Miner Teacher's College near the Howard University campus.

That was 1954, but the memory is still fresh.

This week, 2,000 brothers of Kappa Alpha Psi are back in Washington, and meeting at the Sheraton Washington. And though they've made some progress, the fraternity's social action agenda remains a top priority. Tuesday, for example, about 3,000 fraternity brothers and their families marched to the South African embassy, chanting, "Freedom, yes! Apartheid no!" Three fraternity leaders were arrested at the protest.

But if public policy is vital to the Kappas, it still is only part of a larger ideal of achievement and brotherhood.

When Carter Gilmer pledged Kappa in 1965 at Drake University, he was a young man from an inner-city Chicago high school at a predominantly white college in Iowa. He heard white students discussing their summer houses and trips to Europe and said he didn't know how to relate to them.

In Kappa, he found support. If he needed a ride or a tutor, "there were guys who'd bend over backwards to help you," said Gilmer, who is now a Philadelphia-based chemist with Du Pont.

His experience is not isolated.

Jackie Berry, 25, a second generation Kappa, said referrals from fellow brothers have boosted the family real estate business in Phoenix.

And Myron Terry, 22, from Buford, S.C., has noticed a different kind of brotherhood. "I can wear this fraternity shirt and go anywhere in the United States and meet brothers," he said.

Once a Kappa, always a Kappa. There are 79,000 brothers, among them Urban League President John Jacobs; U.S. Reps. John Conyers Jr. (D-Mich.), George W. Crockett Jr. (D-Mich.), Mervyn M. Dymally (D-Calif.), and Louis Stokes (D-Ohio); D.C. Del. Walter Fauntroy; Eastern Airlines Vice President Hannibal Cox; Grambling College President Joseph B. Johnson; football player Gale Sayers and tennis pro Arthur Ashe.

These leaders serve as inspiration for the younger Kappas, who receive advice and scholarships from the alumni. "Every brother here is about achievement," said Tommie Robinson, who, at 22, is living the Kappa ideal. He maintains a high B grade average, served as president of his fraternity house, and captained the division-winning NCAA football team at Troy State University in Troy, Ala. "I am about achievement," Robinson said. The Old, Old Guard

Earl Dickerson remembers Washington in 1926, when he had to eat his meals in Union Station if he wanted to be served. At 94, he was the oldest Kappa at the meeting this week and founder of the fraternity's second chapter, at the University of Illinois in 1913.

A retired attorney from Chicago, given to quoting Homer and Tennyson, Dickerson remembered his meeting with Elder Washington Diggs, one of the two founders of Kappa Alpha Psi.

"He was a scholar and a teacher and a very serious man who had his eye on the stars," said Dickerson. "He was concerned that blacks go to college and make some effort and achievement so as to prepare them for black leadership."

By 1925, Dickerson had attained the fraternity's highest position, grand polemarch. He traveled to colleges to pitch the fraternity to students and, for the community, arranged picnics, business seminars and discussions of black issues.

There didn't seem to be anyone to help Dickerson when he graduated from the University of Chicago Law School in 1920. He said he was rejected by three white law firms because of his color. After that, he started his own practice, but after just a few months, one of the first black insurance companies hired him as general counsel. In 1955, he was elected president and chief executive officer of what is now Supreme Life Insurance Co. of America Inc.

As the white-haired Dickerson told his story, a group of Kappa brothers from Troy State University asked him to pose with them for a picture. "The stuff I'm reading, he has lived," Robinson said. "It's a thrill to me." The New, New Guard

Timothy Brown, 22, could be considered the Gary Hart of Kappa Alpha Psi, with his campaign for fraternity office stressing youthful leadership. A recent Howard University graduate, Brown just finished his sales training program with Dow Chemical last month.

Brown is aiming for the No. 2 position in the organization, senior grand vice polemarch. He is challenging a man twice his age who is an established fraternity figure, and that has upset quite a few of his brothers. This is a traditional organization, where respectable middle-aged men engage in secret handshakes and wear fraternity pins, rings and sweat suits. As brothers go to the polls today, Brown must overcome the age issue.

If he wins, Brown will push for increased guidance for high school and college students. "We need to put more of an emphasis on training for leadership," he said. "Before we want them to donate time to Kappa Alpha Psi, we want them to get their objectives straight." The Agenda

As the chief executive officer of Kappa Alpha Psi, Grand Polemarch Robert Gordon has one basic goal:

"To save humanity."

It may sound bold, but Gordon believes everything starts with one person. "I'm a little person with a big heart and a big concern about where we're heading," said Gordon.

"Today, the gains that we made 10 years ago are gradually being taken back," said Gordon, referring to the Reagan administration's budget cutbacks on social programs and policy on affirmative action.

At this convention, domestic issues have been overshadowed by concern for Africans, the hungry and the oppressed.

Gordon planned the embassy demonstration with his brothers for nine months. "I wish I didn't have to march," he said, expressing sorrow that the South Africans have continued to oppress blacks.

Several Kappas said the United States, by virtue of its role as a world leader, should impose economic sanctions on the South African government. In his keynote address Sunday, Kappa brother and Los Angeles Mayor Tom Bradley said that while other countries have taken economic action against apartheid, Reagan's policy of "constructive engagement" has made America "the laughingstock" of the world. The Leader

The grand polemarch made a regal appearance before the fraternity's women's auxiliary, The Silhouettes. Their meeting was in progress when one of the women announced his arrival. They stood up and turned around to the back of the room, applauding as he descended the carpeted stairs and strode to the dais.

Gordon's job requires as much public relations as political activism, and this speech was a little of both. He wanted to generate interest in the South Africa protest, which would be held later that afternoon, and he also wanted to praise the Silhouettes.

"The black woman is strong," he told them. "It's just a damn shame -- excuse the expression -- that the black man doesn't appreciate her."

The women applauded.

Gordon continued his message. "I believe that we have an obligation to save the black youth of today . . .

"Somebody is going to push a button and destroy the Earth . . .

"If what is happening in South Africa were happening in Israel, the Jews would be in arms," he said, trying to convince the women to join him in the embassy protest.

Gordon, 44, spends most of his weekends on the road talking to college students, chambers of commerce and others. As his 36-month term draws to a close, he looks forward to returning to his personnel and consulting business in Southfield, Mich.

He is the 24th man to wear the polemarch's pin on his blazer and he expects future polemarchs to continue to lead the brothers' fight for economic parity. "You just look around the world and community and . . . and you see that the economic power base is still in the white community."

"The struggle continues in the black community," he said. A Brotherhood of Reality

By tomorrow, the brothers will have legislated on everything from the fraternity's constitution to matters of public policy. If debate over Kappa election procedures sounds arcane, remember that a deeper bond than networking in business suits keeps these men together.

Ernest Davenport of Silver Spring, Md., offered one vital reason for the brotherhood. The winner of the fraternity's coveted Laurel Wreath award, which he received for his excellence in accounting, Davenport remembered how just three days ago, he was stopped by a white garage attendant who apparently didn't believe he had parking privileges.

"Those are the kind of things that consistently happen to people of color," said Davenport, who was the fourth black CPA in Michigan. He said he has repeatedly found himself fighting for entry to the white coffee klatch groups where informal discussions often yield valuable business tips.

It is a "subtle, insidious, systematic" racism that still exists today, said Davenport, who believes blacks still have a long way to go before they will attain economic power in the United States.

"You have to work at this until the day you die, because every day something happens to you that makes you realize you're not a part of the system."