By Angela Moon

NEW YORK (Reuters) - Apple's market capitalization fell below $500 billion on Thursday as shares of the world's most valuable listed company continued to slide after suffering their worst one-day decline in nearly four years.

Shares of Apple Inc fell to as low as $518.63 on Thursday, declining nearly 10 percent for the week. But for the year, the stock is still up more than 30 percent. At its peak in September the stock was worth $705.07.

Earlier in the day, research firm IDC said Apple's rank in China's smartphone market, which is set to become the world's largest this year, fell to No.6 in the third quarter as it faced tough competition from Chinese brands.

IDC's announcement comes a day after Apple's shares fell more than 6 percent on the Nasdaq, logging its biggest single-day loss in four years and losing $35 billion of its value, on concerns about rivals gaining ground in the mobile devices market.

(Reporting by Angela Moon and Rodrigo Campos; Editing by James Dalgleish)