RICHARD NIXON thought that Lyndon Johnson had his 1968 campaign plane "bugged." Johnson thought Nixon conspired in 1968 to stall Vietnam peace talks to avert an "October surprise." Each used his "secret" to threaten the other.

One who was deeply involved in the tense relationship was Cartha D. ("Deke") DeLoach -- No. 3 in the FBI and liaison with the White House under both presidents. DeLoach is finally breaking his silence in a forthcoming book, "Hoover's FBI," which fills in some of the missing pieces.

DeLoach says that FBI Director J. Edgar Hoover told Nixon shortly after the 1968 election that DeLoach had once planted a bug on his campaign plane. It was untrue, says DeLoach. In any event, DeLoach told me, it would have been virtually impossible to plant a bug on a Secret Service-guarded plane.

But Nixon apparently believed it. He often talked about it to his aides. It may even have served as a justification for the spying on Democrats that led to Watergate.

Former Nixon chief of staff H.R. Haldeman told part of the story in his diary. Nixon, he wrote, discussed "the Johnson bugging process" several times. On Jan. 9, 1973, Nixon said that "if this could be cranked up, LBJ could turn off the whole congressional investigation" of Watergate. The request and the threat were duly conveyed to the LBJ ranch in Texas. According to Haldeman, the ex-president, talking to DeLoach, threatened, in response, to reveal something damaging to Nixon. That something has, until now, been a mystery. Haldeman's diary, as published last year, says, "LBJ got very hot and called Deke and said to him that if the Nixon people are going to play with this, that he would release \. \. \. ."

The next words are "deleted material." It was the only such deletion, and it was made when the diaries were submitted for clearance to the National Security Council during the Carter administration.

That blank is now filled in by DeLoach. In October 1968, President Johnson, having decided not to seek re-election, was hoping to win the presidential election for Vice President Hubert Humphrey by ordering a bombing halt in Vietnam and announcing the opening of peace talks in Paris. Suspecting an effort by the Nixon campaign to use its Saigon contacts to short-circuit the peace move, Johnson had FBI wiretaps placed on the telephones of the South Vietnamese Embassy in Washington and the Watergate apartment of Anna Chennault, the so-called "Dragon Lady," a Nixon supporter. Johnson suspected her of being the channel for messages from the Nixon campaign to Saigon urging South Vietnamese President Nguyen Van Thieu to hold off on peace talks and promising a better deal from Nixon, once elected.

What was overheard in those calls led the White House to order a wider FBI net to be spread. DeLoach says he was told to get telephone company records of calls from the Albuquerque airport during a stopover of the Nixon campaign plane. (This may have been the basis for the rumor that the plane itself had been bugged.) DeLoach ascertained, however, that on the specified day, vice presidential candidate Spiro T. Agnew, not Nixon, had been in Albuquerque. The FBI duly obtained and furnished the White House a list of numbers called -- mostly by Agnew staffers -- during the stopover, and the duration of the calls. But the "smoking gun" came not from wiretaps and telephone company records, but from a much more sensitive source. DeLoach says a White House aide told him of an intercepted and decoded cablegram from South Vietnamese Ambassador Bui Dhien to Saigon, urging Thieu to hold off on peace talks until after the election. This explains the security deletion from Haldeman's diaries. There was no darker intelligence secret than the code-breaking capability of the National Security Agency, especially when targeted against an American ally.

Some of the contents of the decoded messages have become available from other sources. On Oct. 23, 1968, the ambassador cabled, "Many Republican friends have contacted me and encouraged me to stand firm." On Oct. 27, he wrote, "The longer the present situation continues, the more favorable for us. \. \. \. I am regularly in touch with the Nixon entourage."

There was apparently another, and more explicit, cable that confirmed, at least to Johnson's satisfaction, that the Nixon campaign was offering Thieu a better deal after the election if he would stand firm against a cease-fire and peace talks now.

Aware of what was going on, Johnson nevertheless took the risk on Oct. 31, the Thursday before the election, of announcing the bombing halt. On Saturday, Nov. 2, Thieu withdrew from his tentative agreement to peace talks, announcing to his National Assembly that he would not sit down with the Viet Cong. The next day, Sunday, Nixon, fearing that Johnson would denounce him for scuttling the chance for peace, telephoned him with fervent assurances that he had nothing to do with the back channel to Saigon. With two days to go before the election, a furious LBJ offered Humphrey the chance to go public with evidence of the Republican intrigue against peace. This according to LBJ's domestic adviser, Joseph M. Califano.

A close friend and adviser of Humphrey, Max M. Kampelman, says the vice president declined the offer, lacking evidence of Nixon's direct involvement and fearful of the perception of a last-minute political ruse that could backfire. Over that weekend, opinion polls showed Humphrey rapidly closing on Nixon.

Clark Clifford, then secretary of defense, tells a different story in his memoir, "Counsel to the President." He says that Johnson, ambivalent about Humphrey, decided against giving the vice president the evidence of Republican obstruction.

That LBJ would leave two trusted aides like Califano and Clifford with contradictory impressions was not unusual. But Clifford has to be wrong. Kampelman affirmed to me a few days ago that Humphrey told him of having received and declined Johnson's offer.

After the election, Kampelman says, President-elect Nixon privately expressed his appreciation for Humphrey's "patriotism" in not raising the issue of the stalled peace talks. Johnson, unable to win the Vietnam War and frustrated in his "October surprise" peace effort, moved to the LBJ ranch in Texas, with his espionage reports on Nixonian obstruction.

The Nixon-Johnson standoff remained quiescent for four more years until after Nixon's landslide reelection in 1972. In early January 1973, DeLoach says he heard from the LBJ ranch -- the first conversation with the ex-president since he left office. Johnson, DeLoach says, told him that Nixon's people were putting pressure on him to avert a congressional investigation of Watergate and threatening otherwise to expose his surveillance activities during the 1968 campaign.

Johnson had a counter-threat ready -- the decoded message from the South Vietnamese embassy. DeLoach quotes LBJ's words: "If they try to give me trouble, I'll pull that cable from my files and turn the tables on them."

Not many days later, on Jan. 22, 1973, Johnson had his fatal heart attack. President Nixon wrote in his diary that the "sadness" was that LBJ had not been able to establish his place in history by "winning a peace with honor in Vietnam." Daniel Schorr is senior news analyst for National Public Radio.