Under an agreement reached in Libya Dec. 24, a cease-fire between Philippine government troops and the Moro National Liberation Front began Jan. 20, to allow more talks over how to solve the centuries-old grievances of Filipino Moslems in the south.

Moslems, who number about a third of the 6 million people in 13 southern provinces, have asked for local self-government and police powers in their communities. Philippine President Ferdinand Marcos has said he is willing to discuss the demands. Negotiations are scheduled to resume Feb. 5 in Tripoli, Libya, where rebel front leaders have headquarters.

The fighting has occupied more than 100,000 government troops and more than 5,000 regular rebel fighters, cost at least 10,000 casualties over four years and rendered perhaps 500,000 people homeless. Marcos has appeared particularly anxious to settle a war that has hindered his dealings with Arab oil powers on whom the Philippine economy depends.

Government officials here and Moslem leaders in the south appear to agree that a final solution will depend on Libyan leader Muammar Qaddafi's continued willingness to restrain the rebels to whom he has been supplying weapons.

It will also be up to Marcos to persuade army chiefs and Christians in the south that the Moslems will not abuse their new powers.