China's official purchasing managers' index (PMI) for the services sector fell to 55.6 in July from 56.7 in June, while a similar private-sector survey sponsored by HSBC headed in the opposite direction, rising to 53.1 from a 10-month low in June of 52.3.
India's non-manufacturing PMI from HSBC was little changed, slipping to 54.2 in July from 54.3 in June.
With all the PMIs above 50 -- a threshold that divides expansion from contraction -- the surveys are signalling that the services sectors in both China and India are expanding.
In China's case, the fall in the official index was "significant", said Dariusz Kowalcyzk, an economist with Credit Agricole-CIB in Hong Kong.
"However, the 55.6 points level is relatively high, and much better than in the case of manufacturing PMI. It is consistent with solid growth of the services sector, which will put a floor under the whole economy," Kowalcyzk wrote in a client note.
China's fast-growing services industry has so far weathered the global slowdown much better than the country's vast factory sector. The services PMIs have consistently signalled healthy expansion, with the official version hitting a 10-month high in March and the HSBC survey reaching a 19-month high in May.
Two surveys this week on China's manufacturing industry showed PMI readings around 50. Combined, they signalled that growth was stalling or close to stalling for a sector that has been the backbone of China's rise to the world's second biggest economy, after the United States.
HSBC's India manufacturing PMI for July fell to 52.9 from 55.0. It also showed overseas orders for Indian goods fell for the first time in nine months, reflecting the drag on global demand that is hitting all of Asia's exporters.
But even though that index was at its lowest since November, the July number pointed to a relatively healthy pace of growth.
Indian government figures on manufacturing are less flattering, suggesting factory activity is barely growing. Factory output rose 2.5 per cent in June from a year earlier, but that followed two straight months of falls, Thomson Reuters data shows.
It is India's service sector that clearly is providing some encouragement.
"Service sector activity grew at a steady pace in July, with growth in new orders and employment holding up," Leif Eskesen, an economist at HSBC, said of India's services PMI.
The Indian survey showed service sector order books grew at the same clip as in June, prompting businesses to increase their workforces at a similar pace to that of the previous month.
The Indian services PMI did show that firms' confidence is falling, albeit from high levels, as the world economy stutters and the country's government struggles to push ahead long-pending reforms, such as allowing foreign direct investment in the supermarket and airline sectors.
In China, the official services PMI showed that water-borne transport, hotels and postal services all contracted, while Internet software, air transport and residential services remained in growth territory.
"The index indicates the stable economy expansion in the non-manufacturing sector has not been changed," said Cai Jin, a vice president at the China Federation of Logistics and Purchasing (CFLP), which conducts the official survey on behalf of China's National Bureau of Statistics.
Notably, the construction services sub-index rose by 2.3 points to 60.4 in the official PMI, indicating strong growth and reflecting a loosening of the tight restrictions on China's property developers that reined in economic growth in the first half of 2012.
China's top leaders, President Hu Jintao and Premier Wen Jiabao, promised this week to step up policy "fine tuning" in the second half of the year to support the economy.
Beijing has cut interest rates twice and banks' reserve requirements three times since November. Investors expect to see more, though few expect a full-blown stimulus package similar to the one launched during the global financial crisis of 2008/2009.
"The weaker the data now, the bigger the chance for stronger policy response, which eventually should be good for sentiment and for recovery of GDP growth later in H2," Kowalcyzk said.
China's economic growth has eased for six consecutive quarters, due to a domestic credit crunch and the chill of the euro zone debt crisis. However, a Reuters poll in July showed most economists estimate the slowdown bottomed out in the second quarter.
India's ability to boost an economy that grew in the March quarter at a nine-year low of 5.3 per cent is much more limited than China's.
The central bank skipped a rate cut at a review this week, worried that relaxing credit conditions would aggravate inflation, already at high levels.
However, the Indian government is running a heavy fiscal deficit and maintains high subsidies, constraining its ability to provide fresh stimulus.
On top of that, the ruling Congress party has so far failed to garner political support for significant reforms that could drive the economy forward.
Highlighting the country's weak infrastructure, long criticised as crimping economic growth, India suffered two of the worst power blackouts in its history this week. More than half of its 1.2 billion people were without electricity for days.
Copyright @Thomson Reuters 2012