* Euro zone's economic woes deepen in September, PMIs show
* Surveys point to extended Chinese slowdown
* U.S. services sector growth picked up steam last month
* Global stocks, oil head lower; U.S. dollar gains on yen
(Recasts with U.S. services data, adds NEW YORK dateline)
By Andy Bruce and Jonathan Spicer
LONDON/NEW YORK, Oct 3 (Reuters) - The euro zone's economic woes accelerated last month and China's slowdown looked likely to extend to a seventh quarter, surveys on Wednesday showed, while the United States proved the bright spot with better-than-expected news on services and jobs.
Purchasing managers indexes (PMIs) suggested the aggressive actions taken by the world's central banks over the last two months have yet to convince consumers to start spending again.
The chances have dwindled of the euro zone in particular seeing growth again before next year.
Falling new orders and more layoffs marked a worsening decline for euro zone companies, the PMIs showed, while growth of China's normally robust services weakened to an almost two-year low last month.
Economic data in the United States were cheerier in tone, however.
The pace of growth in the massive U.S. services sector picked up more than expected in September on the back of new orders, according to an industry report. And a private sector employment report showed companies added more staff than expected last month, although it revised down the number hired in August.
Growth in the United States has been stronger than elsewhere, yet the world's largest economy remains mired with high unemployment and uncertainty about taxes and government spending next year. Europe's crisis and China's slowdown have already begun to infect the long-stumbling U.S. economic recovery, a grim prospect for world growth.
"Is the global economy heading into another recession? This is now becoming a genuine possibility, given events in recent months," said Gerard Lyons, chief economist at Standard Chartered in London, in a research note.
A good gauge of economic growth, Markit's Eurozone Composite PMI, fell to 46.1 in September from 46.3 in August.
While revised up slightly from a preliminary reading two weeks ago, the index has been stuck below the 50 mark that divides growth and contraction for all but one of the last 13 months.
The data helped send world share markets and oil prices lower on Wednesday, while the euro edged lower against the dollar as traders await Spain's next move to solve its mounting debt problem.
Although the German downturn eased last month, hopes for an imminent recovery in the 17-nation currency bloc were dealt a blow by steeper declines for firms in France, Italy and Spain - the euro zone's three largest economies after Germany.
"There therefore seems little scope for a return to growth in the fourth quarter," said Chris Williamson, chief economist at Markit, which compiles the PMIs.
Outside the euro zone, Britain's services sector growth slowed last month and companies shed jobs for the first time in 10 months.
The data lend weight to a consensus that both the European Central Bank and Bank of England will ease monetary policy further before the end of the year, although few economists believe they will announce anything at their meetings on Thursday.
Graphics: Comparing PMIs and GDP: ADP vs. Labor Department:
'VERY MODERATE GROWTH'
The dollar hit a fresh two-week high against the yen and U.S. stocks briefly paired losses after the Institute for Supply Management said its U.S. services index rose to 55.1 last month from 53.7 in August, topping economists' forecasts for a slight decrease to 53.2.
The forward-looking new orders index jumped, but growth in employment eased, the ISM report showed.
The news comes on the heels of a comparable report on Monday for U.S. manufacturing that was surprisingly strong - another sign of resiliency as Americans prepare to head to the polls for next month's presidential election.
"It looks more like things are heading in the right direction," said William Larkin, fixed income portfolio manager at Massachusetts-based Cabot Money Management. "It is this new reality - we don't have robust growth, we just have very moderate growth."
The ADP National Employment Report, meanwhile, showed private sector companies added 162,000 jobs in September against the 143,000 expected. Still, the August figure was revised down from 201,000 to 189,000.
Economists often refer to the ADP report to fine-tune their expectations for the highly anticipated official payrolls numbers, due on Friday, though it is not always accurate in predicting the outcome. That report is expected to show job growth improved slightly, with employers adding 113,000 jobs.
To kick-start hiring, the U.S. Federal Reserve last month waded deeper into uncharted policy territory with a third and potentially massive program of asset purchases.
THE KNOCK-ON EFFECT
While the U.S. economy has managed to deflect some of the huge uncertainty emanating from Europe, Asian countries that rely heavily on exports to rich Western peers have not fared so well.
China's official services PMI fell to its lowest point since November 2010, as slow growth in manufacturing finally began to feed through to the rest of the economy.
Weak construction services and transport, as well as lackluster new orders overall, pushed the PMI to 53.7 in September from 56.3 in August, signaling economic growth will slow for a seventh quarter.
A Reuters poll last month forecast China's annual economic growth could ease to 7.4 percent in the third quarter, before picking up to 7.6 percent in the final three months. That would likely leave growth for 2012 below 8 percent, its lowest in more than a decade.
News Australia's trade deficit blew out to its widest in 3-1/2 years in August provided a further reminder of the knock-on effect of the uncertainty emanating from Europe, via China.
Falling prices for iron ore and coal ate into export earnings, just the latest sign of how China's slowdown is hurting resource-rich Australia.
Wednesday's data showed the deficit on goods and services yawned out to A$2.03 billion ($2.1 billion) in August, from a revised A$1.5 billion in July. That was far beyond forecasts of a A$700 million shortfall and the largest deficit since March 2008.
"It means the current account deficit will blow out in the quarter and the trend is clearly for further deterioration," said Su-Lin Ong, a senior economist at RBC Capital Markets.
(Additional reporting by Lucy Hornby in Beijing and Wayne Cole in Sydney; Editing by Jeremy Gaunt and Chizu Nomiyama)
Keywords: GLOBAL ECONOMY/