Euro zone businesses had their best month in over two years in August as orders increased for the first time since mid-2011 while growth in China's services sector hit a five-month high, underpinned by new orders and business optimism.
Pockets of weakness remain across the world, however. Data on Wednesday showed Indian services activity shrank in August at its quickest pace since the depths of the global financial crisis.
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Italian services also contracted more than expected and the downturn continued in France.
"The advanced economies have clearly picked up, China is the exception among the major emerging economies but the other emerging economies are still struggling and India in particular," said Andrew Kenningham, senior global economist at Capital Economics.
Emerging economies are particularly vulnerable to a tightening of United States monetary policy, the International Monetary Fund warned in a note prepared for the Group of 20 meeting in St. Petersburg this week.
Markets are preparing for the Federal Reserve to begin slowing down its huge bond-buying programme this month as the U.S. recovery remains on track.
The U.S. Institute of Supply Management is due to publish its PMI for U.S. services on Wednesday and a Reuters poll predicted a dip to 55.0 from July's 56.0. A sister survey on Tuesday covering factories showed a surprise upturn.
Markit's Eurozone Composite Purchasing Managers Index (PMI) rose to 51.5 last month from 50.5 in July, its highest reading since June 2011. The headline figure was revised down a touch from a preliminary reading of 51.7.
Anything over 50 indicates expansion.
A sub-index covering new business rose to 51.0, the first time it has been above the 50-mark that separates growth from contraction since July 2011.
But there are still major differences between Europe's two most important economies. The composite PMI for Germany, the euro zone's largest, jumped to a seven-month high of 53.5, but the French PMI dipped to 48.8 from 49.1.
Businesses' optimism about the future also rose to a 17-month high but firms were not yet confident enough to start hiring again. They cut staff for the 20th consecutive month, and at a faster pace than in July.
Across the channel, a rush of new business last month drove the fastest growth in Britain's services sector for more than six years, challenging the Bank of England's cautious outlook for the economy.
It's services PMI beat forecasts with a rise to 60.5.
Led by firm U.S. growth, the outlook is gradually improving for advanced economies and even crisis-weary Europe is at last joining the recovery, the OECD said on Tuesday, but warned a slowdown in many emerging economies meant global growth would remain sluggish.
The Chinese Markit/HSBC Services Purchasing Managers' Index (PMI) climbed to 52.8 in August after seasonal adjustments, up from July's 51.3 and the highest since March.
Qu Hongbin, an HSBC economist, cited new business growth as the key driver of the PMI and expected the momentum to be sustained.
"A rebound in manufacturing output is expected to support service industry growth in the coming months," Qu said.
Any improvement will cheer investors as fears of a sharp slowdown in the world's second largest economy had kept markets in check but the good news will be tempered by a slowdown in India, Asia's third largest economy.
Having fallen below the 50-mark in July for the first time in nearly two years India's services PMI slipped further last month and with a survey of factories published on Monday showing activity shrank for the first time since early 2009, the picture is grim.
India's economic growth has almost halved in the past two years and the economy grew 4.4 percent in April-June, its slowest quarterly growth rate since early 2009.
The PMIs suggest more trouble ahead as the government and central bank grapple with a currency crisis that has battered the rupee to record lows against the dollar, with no expectations or signs that it will rally any time soon.
"The weak run is set to continue with macroeconomic uncertainty and tighter financial conditions weighing on growth," said Leif Eskesen, HSBC's chief India economist.