Late on April 4, the United States intercepted a message from the Libyan People's Bureau in East Berlin to headquarters in Tripoli telling Libyan authorities that they "will be very happy when you see the headlines tomorrow."

A few hours later, in the early hours of April 5, the United States intercepted a second message from East Berlin to Tripoli reporting that an operation was "happening now" that would not be traceable to the People's Bureau.

That second message, only a few lines long, was sent within 10 minutes of the detonation of a bomb at the La Belle discotheque in West Berlin that killed one American and injured more than 200 people. The blast occurred at 1:49 a.m. Berlin time. Bomb experts subsequently determined that the timer on the device was probably accurate within about 10 minutes.

These two intercepts were the key elements in an intelligence puzzle that, when pieced together, comprised what President Reagan has called the "irrefutable" evidence of Libyan involvement in the La Belle bombing.

Taken individually, the messages were somewhat ambiguous, but their timing and cumulative impact left no real doubt in the minds of senior American officials that they could rightly blame Muammar Qaddafi's Libya for the bombing, informed sources said.

Half a dozen sources familiar with the intercepted messages said that taken together, their impact was totally convincing because they provided the elements intelligence analysts consider crucial: a motive, an order, a time and place and an after-action report.

Sources said that there was no message from Tripoli specifically ordering the bombing of the La Belle disco by name or ordering an operation on a given day. But a March 25 cable from Libya to eight People's Bureaus including East Berlin, which was intercepted by the National Security Agency, directed that the bureaus be ready to undertake operations, attacks or the "plan" against American targets and facilities.

One Libyan message mentioned that American military personnel tended to congregate at specific bars, suggesting that such social gathering places would present a desirable target of opportunity, according to one source.

In addition to East Berlin, the three-line message of March 25 was sent to People's Bureaus -- the Libyan equivalent of embassies -- in Paris, Rome, Madrid and four other European capitals.

These messages came a day after Libya fired missiles at U.S. carrier-based planes operating in the Gulf of Sidra; the United States responded by firing at a Libyan missile site and sinking at least two Libyan patrol boats.

Sources said the United States believes Tripoli normally does not become involved in picking specific targets or times for terrorist operations, under the theory that the People's Bureaus and Libyan diplomatic personnel on the scene can do this best. In addition, the sources said, the Libyans are aware that the United States has been able to intercept and decode its diplomatic traffic, and on occasion Libya has used couriers to deliver sensitive information.

The March 25 message was not sent to London, presumably because Britain broke diplomatic relations with Libya in 1984 and the London People's Bureau was closed. One source said that when the Libyan evidence was presented to the British government earlier this month, authorities there were elated that the Libyans apparently had no presence in London from which to conduct terrorist operations.

Britain broke diplomatic relations after a policewoman was fatally shot in April 1984 outside the People's Bureau in London. Intercepted diplomatic messages showed that Tripoli had encouraged and supported the incident, sources said.

U.S. officials privately expressed great pride in what one called this "intelligence coup." As the North Atlantic Treaty Organization commander, Gen. Bernard W. Rogers, said in a speech in Atlanta on April 9, the intelligence provided "indisputable evidence" of Libyan responsibility and the United States was almost able to warn GIs to vacate the La Belle disco minutes before the explosion. "We were about 15 minutes too late," Rogers said.

NSA officials, however, were alarmed by Rogers' statement and an earlier one by the U.S. ambassador to West Germany, Richard R. Burt, about the intelligence information tying Libya to the bombing. The aency subsequently notified the recipients of these top-secret intercepts that public revelations of their contents were severely hampering its ability to intercept Libyan cables.