By Summer Zhen

HONG KONG, Jan 7 (Reuters) - China and Hong Kong shares fell broadly on Tuesday due to worries about foreign investors further reducing their holding in local stocks after the US added tech giant Tencent and others to a list of firms that it said work with China's military.

** China's blue-chip CSI300 Index had dropped 0.08% by the lunch break, while the Shanghai Composite Index

had fallen 0.32%, both on track for a five-day losing streak.

** Hong Kong benchmark Hang Seng declined 1.9%.

** The U.S. Defense Department said on Monday it has added Tencent and battery maker CATL to a list of firms allegedly aiding Beijing's military.

** The list included chipmaker Changxin Memory Technologies, Quectel Wireless and drone maker Autel Robotics

.

** By midday, Hang Seng heavyweight Tencent had slumped 6.8% and was on course for a fifth straight session of declines. It also weighed on the tech index , which declined 2.4%.

** On the mainland, CATL dropped 2.8%, Quectel tumbled 8.3% and Autel Robotics retreated 5.3%.

** Analysts said although the inclusion should not have a material impact on the companies, the move would keep investors on the sidelines.

** "The move implies continued volatility particularly ahead of (U.S. President-elect Donald) Trump's promise of added tariffs," said Kai Wang, Asia equity market strategist at Morningstar.

** Another concern was the move may prevent certain funds from owning the stocks due to geopolitical risks, which would mean they could go underweight on those stocks even more, Kai Wang said.

** By sector, healthcare sub-index down 2.02% to lead the decline in A-shares.

** The smaller Shenzhen index was down 0.05%, the start-up board ChiNext Composite index was weaker by 0.55% and Shanghai's tech-focused STAR50 index was up 0.58%​.

** Around the region, MSCI's Asia ex-Japan stock index

was firmer by 0.07%, while Japan's Nikkei index

was up 2.43%.

** Chinese ADRs fell 1.16% overnight.

(Reporting by Summer Zhen; Editing by Savio D'Souza)

((summer.zhen@thomsonreuters.com; 852-3462-7739;))