THE BESTSELLING book Roots , Alex Haley's historical reconstruction of how his family came from relative freedom in Africa to certain slavery in America, and then from slavery to relative freedom today, has spurred many black Americans to think about and search out their own roots.

A few years ago most blacks were either ashamed or afraid to tell the story of their struggle for survival against enormous odds. Their reticence derived in part from the frequent ugliness of their stories.

On these four pages are the true stores of eight Washingtonians who not only survived exploitation but went on to achieve prominence in a world dominated by whites.

Clifford Alexander Jr., the Secretary of the Army, a Washington lawyer who ran against Mayor Walter Washington in 1974, knows that his mother's family came from North Carolina, but the specific lineage is obscure. "We always heard stories about American Indians and intermarriage with the whites down there," he says. "They were great stories about who they were the illegitimate children of, but none of it can be documented." His grandfather, Nathan McAllister, came north from North Carolina to Springfield, Massachusetts, where he worked as a waiter on the New Haven Railroad for years. Then he wandered down to Yonkers where Alexander's mother was born.

Edith McAllister was a civil rights activist in the 1940s. She ran the Mayor's Committee on Unity, a forerunner of equal opportunity groups of today, and was largely responsible for breaking down the color barriers in organized baseball in New York and for changing the discriminatory housing codes.

in the early '40s she organized economic boycotts against organizations in Harlem that would not hire blacks. She also was the first black woman to be appointed a residential elector (for Truman in 1948), and later she became the head of the Mayor's Advisory Council.

Clifford Alexander Sr. came to this country from Jamaica in 1919 with about $30 in his pocket. He got a job as a waiter on a pleasure boat in the Great Lakes, and later moved to New York where he was a waiter at the Cornell Club and took courses at night.

He went from managing the Harlem YMCA to managing apartment complexes and, after he turned 65, to managing a bank. In April he will be 80.

The Alexander family history extends back little further than Clifford Sr. Clifford Jr. says his grandfather was killed in an earthquake when his father was only two years old. His grandmother died when Alexander was small. The only tale to survive her is that she gave her son a cow (in Jamaica) when he married Edith McAllister.