The 19-year-old Organization of African Unity faced the threat of dissolution today as African leaders failed for the second time in four months to convene their annual summit conference on schedule.

Presidents and prime ministers met throughout the night to resolve the issue of representation for the war-battered central African nation of Chad, but still had not come up with an acceptable formula, Peter Onu, assistant OAU secretary general, told reporters in a late night press conference. Onu declined to discuss what solutions are being considered.

The summit was originally scheduled for August but was postponed because of a dispute over membership of the former Spanish colony of Western Sahara, a vast, sparsely inhabited desert territory in northwest Africa being fought over by Morocco and guerrillas of the Polisario front supported by Libya and Algeria. A boycott by 21 nations made it impossible to gather the quorum of 34 necessary for the summit to open.

Many African diplomats fear that a second cancellation of the summit could lead to the break-up of the OAU, the world's largest regional organization.

Dissolution of the OAU would be a sharp setback to the continent's efforts to bring black-majority rule to Namibia and South Africa, the last two outposts of white dominance in Africa. It could also lead to the formal division of Africa along ideological lines with separate pro-Soviet and pro-Western blocs.

On the Chad issue, most African states have lined up on the side of Hissene Habre, whose guerrilla forces won control of most of the country, including the capital Ndjamena, earlier this year.

Libyan leader Muammar Qaddafi, who is host for the conference, has refused to allow Habre's pro-Western government to be represented. He is supporting the man Habre ousted, former president Goukouni Oueddei, whom Qaddafi's Army originally helped to install in power.

As a day of informal meetings wore on, the mercurial Qaddafi kept everyone guessing about the fate of the summit, but there were indications that African delegates were becoming annoyed at his tactics.

One said Qaddafi was becoming increasingly isolated as the leaders felt the Chad issue should not prevent the summit from going ahead. The delegate, from a country that lined up with Qaddafi on the Western Sahara issue in August, said that if the meeting were held anywhere else but Libya the question of Chadian representation would not be an issue.

Three nations -- Egypt, Sudan and Somalia -- have refused to attend the summit because of opposition to Qaddafi. Another, Upper Volta, is absent because of a coup earlier this month. At least 15 countries have said they will refuse to take part unless Habre's delegation is seated.

Only 29 nations have registered for the conference, but about a dozen others are present and prepared to participate if an acceptable solution is reached on Chad.

There were reports that attempts were being made to reach a compromise under which Chad's seat would not be occupied, but it remained to be seen whether the 15 nations that have threatened a boycott would go along with such a solution.

Shortly before the 5 p.m. scheduled start of the summit, Goukouni's vice president, Abdul Kader Kamougue, demanded at a news conference that his delegation be seated.

In Lagos, the Nigerian government issued a communique saying that President Shehu Shagari and Kenyan President Daniel arap Moi, the outgoing chairman of the OAU, had agreed that they would not attend a summit unless Habre's delegation is seated.

Libyan television has given Goukouni's presence in Tripoli prominent coverage and tonight it said that his was the only legitimate representative of Chad.

Although he has yet to be able to stage a summit that would make him the nominal leader of Africa, Qaddafi has used the presence of so many African leaders as a platform for his anti-Americanism.

As heads of state or government arrived at the airport, Qaddafi accompanied them to a nearby cemetery where a nine-year-old Libyan girl was buried in 1958 after being killed in an accident involving U.S. military personnel then stationed in Libya.

Qaddafi explained to each leader that the grave was an example of "American imperialism and terrorism."