* KOSPI falls, foreigners net sellers

* Korean won strengthens against dollar

* South Korea benchmark bond yield rises

SEOUL, Dec 26 (Reuters) - Round-up of South Korean financial markets:

** Korean shares started the week on a muted tone on Tuesday in thin volumes after the Christmas holiday weekend, following an eighth straight week of gains last week on optimism over Federal Reserve interest rate cuts next year. The won strengthened, while the benchmark bond yield rose.

** The benchmark KOSPI fell 1.32 points, or 0.05%, to 2,598.19 by 00:45 GMT.

** Among index heavyweights, chipmaker Samsung Electronics rose 0.53% and peer SK Hynix gained 0.14%, while battery maker LG Energy Solution slid 0.24%. ** Hyundai Motor was flat and sister automaker Kia Corp lost 0.42%, while search engine Naver and instant messenger Kakao were up 0.93% and unchanged, respectively.

** Of the total 936 traded issues, 338 shares advanced, while 526 declined.

** Foreigners were net sellers of shares worth 11.5 billion won ($8.86 million) on the main board on Tuesday.

** The won was quoted at 1,298.8 per dollar on the onshore settlement platform, 0.32% higher than its previous close at 1,303.0.

** In offshore trading, the won was quoted at 1,298.4 per dollar, down 0.2% on the day, while in non-deliverable forward trading its one-month contract was quoted at 1,295.8.

** The KOSPI has risen 16.18% so far this year, and gained 7.9% in the previous 30 trading sessions.

** The won has lost 2.6% against the dollar so far this year. ** In money and debt markets, March futures on three-year treasury bonds fell 0.03 point to 105.14.

** The most liquid three-year Korean treasury bond yield fell by 0.2 basis points to 3.233%, while the benchmark 10-year yield rose by 0.2 basis points to 3.310%. ($1 = 1,298.4400 won) (Reporting by Cynthia Kim; Editing by Sonia Cheema)