China, which claims economic and territorial rights in almost the entire body of water, has boycotted the proceedings and rejects the court`s authority in the case.
But experts say the ruling could influence other cases in the heated South China Sea dispute - involving Vietnam, Taiwan, Malaysia, Brunei and other countries. Indonesia has signaled it may also go to the courts.
The claims by an increasingly assertive China - based on specks of rock that it owns, dotted throughout the area with names like Scarborough Shoal and Mischief Reef - have triggered protests among its neighbors around the Pacific rim.
The United States, traditionally the region`s dominant security player, also objects to China`s moves, sending military aircraft to survey China`s development activities.
The court, set up in 1899 as one of the first international judicial institutions, said it would hear arguments including one contending that several South China Sea reefs and shoals were not a significant enough basis for China`s claims.
Court rulings are supposed to be binding on its member countries, which include China. But the tribunal has no powers of enforcement and its rulings have been ignored before.
The Philippines` case is based on the United Nations Convention on the Law of the Sea (UNCLOS) - a pact that does not cover matters of sovereignty, but outlines a system of territory and economic zones that can be claimed from features such as islands, rocks and reefs.
The Philippines will make submissions on 15 claims during the proceedings, which are expected to last around a week.
China says the legal challenge could delay a negotiated settlement between the two countries.
Japan, Vietnam, Thailand and Malaysia will also observe the pleadings, which will run until Nov. 30 in private. A final ruling is expected in mid-2016.
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