Elmo Zumwalt III, who in a tragic irony was exposed to Agent Orange ordered dropped on the Vietnam jungles by his father, died Saturday of cancer, a family spokeswoman said. He was 42.

His father, Adm. Elmo Zumwalt Jr., and his brother, Jim Zumwalt, were at his side when he died at his home in Fayetteville at 6:30 a.m., the spokeswoman said. Zumwalt III had suffered from Hodgkin's disease and lymphoma, cancers linked to the toxic substance Agent Orange.The spokeswoman said a memorial service for Zumwalt III, an attorney, will be held Wednesday in Fayetteville.

In Washington, a White House spokesman said, "The president and Mrs. Reagan are deeply saddened and extend their prayers to the Zumwalt family."

When Zumwalt's father, the American naval commander in Vietnam, ordered the use of Agent Orange to defoliate the guerrilla-infested jungles in the Southeast Asian nation, the toxic substance was thought harmless to humans.

Later, it was learned the defoliant causes birth defects and cancers. Zumwalt III and the son he had after the war were both victims of that toxicity.

But the admiral and his son said they would not rewrite history if given the chance, despite the younger Zumwalt's battles with four rounds of cancer and his son's severe attention deficit disorder.

"I definitely believe my son would not have had an additional 20 years of life had we not used it," Zumwalt Jr. said in a telephone interview Saturday from his son's home. He contended "thousands who are alive today would not be" if the defoliant had not been sprayed.

"Both my son and I believe the horrible casualty rates had to be reduced. Thousands of lives were saved," he said, adding he does not doubt a link between Agent Orange and tragic health consequences.

"Both my son and I made it clear that although the medical evidence is not yet absolutely definitive, we believe there is no doubt that the Agent Orange has caused cancer and birth defects for the population that was exposed," he said.

Zumwalt III once said he did not fault his father for ordering the use of the chemical.

"I do not second guess the decisions Dad made in Vietnam, nor do I doubt for a minute that the saving of human life was always his first priority in his conduct of the war," Zumwalt III said. "I have the greatest love and admiration for him as a man, and the deepest respect for him as a military leader."

A lawsuit, brought by many Vietnam veterans suffering the adverse affects of Agent Orange, recently was settled for $180 million without any admission of guilt by the defoliant's manufacturers. Zumwalt Jr. said about 250,000 veterans were exposed to the chemical.

Adm. Zumwalt, who retired from the Navy in 1974, said the pain of seeing his son dying of cancer after winning the battles against a defective heart and polio caused inexorable heartbreak - but did not change his mind about Agent Orange.

The father-son story of the battle with cancer was chronicled in 1986 in "My Father, My Son," a book the two men wrote with author John Pekkanen.

Zumwalt III is survived by his father, his wife, Kathy, his son, Elmo Russell Zumwalt IV, his daughter, Maya, and his brother and two sisters.