SEOUL, July 2 South Korea's main KOSPI share index was down 0.08 percent at 1,854.17 as of 0252 GMT. The index opened up 0.3 percent at 0001 GMT.
Stocks on the move on Tuesday include:
**AUTO SHARES SLUMP**
Auto stocks slumped after they reported disappointing car sales in June, sparking a foreign sell-off after recent sharp gains.
"Foreign investors appear to be worried about less-than-expected sales from domestic plants despite the resumption of weekend work in South Korea," said Eric Choi, an analyst at Shinhan Investment Corp.
Hyundai Motor and Kia Motors saw their shipments from South Korean factories decline 7 percent and 8 percent respectively in June from a year earlier, although their overseas production offset the falls.
Hyundai and Kia are floundering in the domestic market, as free-trade deals allow foreign carmakers to slash prices and boost sales.
Hyundai Motor, South Korea's biggest automaker, slid 3.6 percent, extending losses into a second session after jumping 12 percent last week. UBS and Deutsche Securities were top sellers of its shares.
Hyundai Motor affiliates also lost ground, with Kia Motors diving 5.2 percent and Hyundai Mobis losing 3.1 percent.
**SK HYNIX SHARES TUMBLE AMID PROFIT-TAKING**
Shares in memory chip maker SK Hynix Inc tumbled on profit-taking after four straight sessions of gains, weighed also by views that its earnings will peak in the third quarter, analysts said.
SK Hynix shares have risen 22.5 percent so far this year as of Monday's close, compared with the broader KOSPI's 7.1 percent fall.
"Demand (for shares) has weakened following a prolonged rally this year. Company earnings are also expected to peak out in third quarter as are chip prices," said Jeff Kang, an analyst at Daishin Securities.
"Shares were ripe for profit-taking, though it came a bit earlier than we had expected," Kang added.
Shares in SK Hynix were down 6 percent as of 0101 GMT, with Kiwoom Securities and Citi among top sellers of the shares.
**STX GROUP SHARES RISE ON POSSIBLE CREDITOR SUPPORT **
Shares in STX Offshore & Shipbuilding Co Ltd rose by more than 12 percent after a local newspaper reported STX Offshore's creditors may inject an extra 1.05 trillion won ($927 million) this year to rescue the debt-laden shipbuilder.
A preliminary plan to support STX Offshore, viewed by creditors on Monday, proposed creditors inject the funds by end-2013, plus an additional 1.1 trillion won in rescue funds between 2014 and 2017, according to the Korea Economic Daily on Tuesday.
STX Offshore's creditors have already provided 850 billion won in rescue funds to the shipbuilder after it sought a corporate restructuring agreement in April.
Creditors' due diligence found STX Offshore's going-concern value outweighed its liquidation value by about 910 billion won, the report said.
Shares in STX Offshore's major shareholder STX Corp rose by more than 8 percent, while affiliate bulk shipper STX Pan Ocean Co Ltd rose more than 5 percent before paring gains.
A spokesman for STX Offshore's main creditor, Korea Development Bank, confirmed Monday's creditors' meeting but declined to give details. An STX spokesman declined comment.
($1 = 1132.3500 Korean won) (Reporting by Hyunjoo Jin, Jungyoun Park and Joyce Lee; Editing by Jijo Jacob and Prateek Chatterjee)