SHANGHAI, Sept 5 (Reuters) - China stocks closed lower on Tuesday after a survey showed that domestic services activity expanded at the slowest pace in eight months in August and as optimism spurred by Beijing's latest stimulus measures also appeared to lose its initial euphoria.

** China's blue-chip CSI 300 Index and the Shanghai Composite Index dropped 0.7% each at market close.

** Hong Kong's Hang Seng Index and the Hang Seng China Enterprises Index lost 2.1% each.

** The Caixin/S&P Global services purchasing managers' index (PMI) dropped to 51.8 in August from 54.1 in July, as weak demand continued to dog the world's second-largest economy and stimulus failed to meaningfully revive consumption.

** Beijing has released a slew of measures in recent months to revive slowing growth and boost market confidence, including easing some borrowing rules to aid homebuyers and reducing trading costs on the stock market.

** The measures drove the stock market off a nine-month low, but some analysts worry that the rally would not last.

** "These measures mark a significant step towards stimulating the property sector and the broader economy, but we think they are still not enough," said Ting Lu, chief China economist at Nomura. "Beijing may have to introduce more aggressive easing measures to ensure a real recovery. "

** The Hang Seng Mainland Properties Index and China's CSI 300 Real Estate Index lost 2.8% and 2.2%, respectively, as some investors locked in profits following a recent rally.

** Most sectors in onshore markets finished lower. Shares in financials and construction engineering were down roughly 1.4% each, while coal miners added 0.6%.

** Tech giants listed in Hong Kong declined 2.6%.

** Foreign investors have sold a net 4.6 billion yuan ($630.40 million) of Chinese shares via the Stock Connect on Tuesday.

($1 = 7.2970 Chinese yuan) (Reporting by Shanghai Newsroom; Editing by Sherry Jacob-Phillips)