The wives of presidents are members of America's most exclusive sorority, and this week two of them intervened to help out a man who once ran the household they both have shared.

Jacqueline Onassis, the widow of John F. Kennedy and now an editor at Doubleday in New York, called Nancy Reagan's staff director on Tuesday and asked if the White House would grant an exception so that J. Bernard West, a White House usher under six presidents, could be buried in Arlington National Cemetery. Unless the president decides otherwise, Arlington accepts only career military people or recipients of military awards.

The exception was quickly granted, and yesterday morning Nancy Reagan called Onassis at her office in New York to tell her so. They talked for 10 minutes, according to Sheila Tate, Nancy Reagan's press secretary. "They both expressed an interest in meeting each other," Tate said. She added that the first lady told her afterward that "we called each other Jackie and Nancy, even though we've never met. We feel like we know each other."

Nancy Reagan also intervened in another Arlington burial yesterday--that of ABC anchor Frank Reynolds, who died early yesterday.

Mrs. Reagan called Reynolds' wife, Henrietta, to express her condolences, and Henrietta asked if the president could grant an exception so that her husband could be buried in Arlington--his last request. The president said he would, but as it turned out, Reynolds was eligible anyway because he had received a Purple Heart for his Army service during World War II. Nancy Reagan, Tate said, "is very upset about Frank's death. She was crying when she talked to me this morning."

The Reynoldses have been personal friends of the Reagans since 1976, and have been to private dinners at the White House.

Speaking of the first lady's conversation with Onassis, Tate said Reagan and Onassis have had four or five phone conversations and exchanged as many notes--including one Onassis sent when Ronald Reagan was shot.

While Nancy Reagan has never said so publicly, it is said that she wants to be seen as Onassis was as first lady: a stylish trend-setter, admired for the tone she brought to the White House. Although Mrs. Reagan has come in contact with other first ladies--Rosalynn Carter, Betty Ford and Lady Bird Johnson--at official functions, Tate said she "probably" has talked to Onassis more regularly than the others.

Tate also said Onassis told Nancy Reagan that she thought the Williamsburg economic summit in May had been done "beautifully."

West, who died Monday, began his White House career in 1941. He became chief usher in 1957, remaining in that job until the Nixon administration. In 1973 he wrote the best-seller "Upstairs at the White House." Onassis was asked by one of his friends to intercede for the burial. She first called the office of her brother-in-law, Sen. Edward Kennedy (D-Mass.), and she was told, in the words of spokesman Melody Miller, that the best way to do it would be by going "first lady to first lady."

West will be buried Friday afternoon, and Reynolds on Saturday.