Basis for PRC's and ROC's claims
The PRC and ROC base their claims on the belief that the islands have been an integral part of China for nearly two thousand years and that neighboring countries and European Powers took advantage of China's poor condition and diversity to impinge on its sovereignty.
China claims to have discovered the islands in the Han Dynasty in 2 BC. The islands were claimed to have been marked on maps compiled during the time of Eastern Han Dynasty and Eastern Wu (one of the Three Kingdoms). Since the Yuan Dynasty in the 12th century, several islands that may be the Spratlys have been labeled as Chinese territory, followed by the Ming Dynasty and the Qing Dynasty from the 13th to 19th Century. In 1755, archaeological surveys the remains of Chinese pottery and coins have been found in the islands and are cited as proof for the PRC claim.
In addition, the PRC's military presence ensures a tangible claim to other potential challengers of sovereignty over at least those inhabited areas.
Criticisms to the PRC's and ROC's claims
Surveying an area without establishing a civilization there or a military garrison does not hold the same political weight as staking an official claim. However, the PRC's claim to the Spratly Islands is grounded in the philosophy that since they were present there first they rightly have sovereignty.
Many of these claims to sovereignty come directly from the Ministry of Foreign Affairs of the People's Republic of China. There is also doubt as to whether these sources state a claim of sovereignty or simply mention the Spratlys alongside other foreign lands.
Claims of pottery being found are mostly shipwrecked treasure from Chinese galleons that sailed through the area and did not necessarily come from anyone who inhabited or even visited the islands.
Source:
Spratly Islands dispute - Wikipedia, the free encyclopedia