The gaps and contradictions in the Billy Carter story as hesitantly put forward so far by the White House will become the major focus of Senate investigators if past major congressional investigations are any guide.

Legislators have already joined reporters in asking why it has taken so long for the complete story to emerge. But an analysis of what has already been said shows the pitfalls that lie ahead for President Carter, his White House aides and officials in the administration who are bound to be caught up in what is likely to be an ever-expanding inquiry.

The biggest unknowns are the Libya-related activities since last November of the central figure in the drama, the president's brother.

The White House, according to Carter, aides, does not know what Billy Carter and his fellow agent for the Libyans, Henry (Randy) Coleman, did that led up to Libyan Charge d'affaires Ali Houderi delivering two checks totaling $220,000 in January and April of this year.

Presidential aides profess not to know what Coleman, the man who actually picked up the money in Washington for the president's brother, was doing in Libya in the months just preceding the delivery of each check.

Billy Carter, on the Advice of his lawyers, has generally refused to discuss the matter. In his flip way, however, there have been hints that he may cause a flurry when he talks.

He reportedly told reporters last week in New York they would be surprised when they discovered whose idea it was to have national security affairs adviser Zbigniew Brzezinski contact him. That remark led eventually to White House press secretary Jody Powell identifying Rosalynn Carter as one who called Billy and may have suggestered the idea to the president.

The July 22 White House "white paper," which Powell described that day as "a recounting of most of the pertinent details to the extent that we could determine them," provides only an outline of the affair.

A close look at two events that were left out of that recounting shows how congressional investigators may proceed.

Five days after the now-famous Nov. 27 Brzezinski-Houderi-Billy Carter meeting at the White House, a mob of Libyans stormed the U.S. Embassy in Tripoli and burned it down.

On Dec. 5, Houderi was called to the State Department and given a stiff protest from the United States that included the threat that relations between the two countries could be severed if the Libyans permitted another such action to occur against the American government.

The very next day, Dec. 6, Houderi went to the White House and met the president for the first time since his arrival in Washington Sept. 1. Brzezinski was present at the meeting.

Powell has given two stories as to how this unusual session came about. The first -- provided to The Post July 23 -- said Houderi asked for the session. On July 24, Powell reversed himself and said the president arranged it.

Powell had to confess, however, that his second version on July 24 was being offered even though he had yet to check the president's own dictated recollection of the meeting.

After his Dec. 6 session with Carter, Houderi flew to Tripopli. Four days later, his boss, Libyan leader Muammar Qaddafi, gave an interview to The New York times in which he said he had "received . . . assurances in the last few days through unofficial but reliable channels from President Carter." The assurance, according to Qaddafi, were that the U.S. policy on the Middle East would shift toward "a more neutral posture" if the president were reelected.

As a result, the Libyan leader said he was dropping his earlier threat to cut back on oil exports to the United States.

At the time, the White House denied any policy changed toward Libya.

On Dec. 12, Houderi was back in Washington and met again with Brzezinski. Reports on that session have been vague so far, but congressional investigators most certainly will be after Brzezinski's notes on the session.

Within the month, Billy Carter's sidekick, Coleman, was on his way to Libya -- a trip paid for by the Libyans and listed on the president's brother's registration form as being part of his activities as a foreign agent.

The episode involving Attorney General Benjamin R. Civiletti and the president also promises to be a prime target for investigators.

On June 17, Civiletti had a brief exchange with the president with regard to the Billy Carter situation. In it he told the president that his brother was "foolish for not having registered long ago." He then responded to a presidential question on what would happen if Billy Carter registered by saying that "if a person tells the truth and registers, the previous failure to register has not been prosecutable."

The president apparently made some notation of the Civiletti conversation, and the attorney general remembered it. Whether he made a record of it remains to be seen.

The July 22 "white paper," put together just over a month after the Civiletti exchange, said there had been no contact between Justice and the White House "concerning the conduct of the investigation." The June 17 "contact" had not concerned itself with the "conduct of the investigation," so the white paper is artfully correct.

But in putting that white paper together, did the White House call Civiletti? On July 15, White House counsel Lloyd Cutler was quoted as saying, "There have been no contacts of any kind in either direction with the attorney general about the matter. It's never been discussed."

"It" was the Justice Department investigation. The contact was more limited, but it did take place.

"Did you talk to the president about Billy Carter?" Civiletti was asked at his July 24 news conference.

The attorney general was on the spot. Two days earlier, the White House white paper had flatly said there had been no "contacts" between the White House and Justice Department "concerning the conduct of the investigation."

When the question came up, Civiletti responded "No" as to whether he had ever had a "talk" with the president about Billy Carter.

Had the questioner stopped there, Civiletti would have been caught in a flat misstatement with no way to try to get out of it. The June 17 exchange most certanily had been a "talk," brief as it had been described..

Civiletti was quickly asked however, "Why not?" meaning why had he not talked to the president about his brother.

The attorney general's answer has since provided his only defense in recent days.

"We don't make it a practice of discussing investigations with the White House," he said.

Was that an artful expansion of the question, implying that only a long "discussion" with the president rather than the actual short exchange was what the reporter was asking about?

If Civiletti prepared for his July 24 press conference as most Cabinet members do, he probably had a practice session with his aides, and no doubt such a question was posed. They all would be fair game for congressional investigators -- along with any record of that session.