* Russian stocks hit all-time high
* Asian heavyweights shut for Lunar New Year
* PMI data across EM countries reflect slowing signs
Feb 5 (Reuters) - Emerging market stocks steadied on Tuesday with Russian stocks testing all-time highs, while developing world currencies were mixed even as the U.S. Federal Reserve's dovish tone continued to build appetite for riskier assets.
MSCI's index for emerging market stocks neared five-month highs with indexes in Moscow and Johannesburg leading gains. But trading remained light in Asia, with markets in greater China, Taiwan, Hong Kong, South Korea and Indonesia all closed for the Lunar New Year.
EM assets have benefit so far his year from the U.S. central bank's signals to ease monetary policy, but weak data from major economies in the group continue to weigh on sentiment.
"For the short-term, the outlook for EM assets may now be tilted in a bullish direction," said Cristian Maggio, Head of Emerging Markets Strategy at TD Securities.
"The underlying macro trend, however, continues to look bleak. Economic activity in EMs has weakened over the course of 2018, and certain markets now have indicators of industrial and manufacturing activity contracting," he added.
A slew of manufacturing and service activity data released on the day reflected mixed prospects, with numbers in Russia showing progress but those in India, South Africa and eastern Europe reflecting signs of slowdown.
Stocks in Moscow's MOEX index, hit an all-time high as energy shares rallied on higher oil prices and after data from a private survey showed Russia's services sector continued to grow in January at one of the strongest paces in the last six years.
The rouble reversed course to shed earlier losses after the central bank lowered foreign currency buying purchases for February.
Indexes in India flitted between negative and positive territory as investors kept a cautious stance ahead of the three-day central bank policy meet, while the rupee slid marginally.
Growth in India's dominant services sector weakened for a second month in January although firms accelerated hiring despite waning demand, a private survey showed on Tuesday.
"Should data for services carry on a downward path, we could see a slowdown in GDP expansion in the final quarter of fiscal year 2018," said Pollyanna De Lima, principal economist at HIS Markit.
Equities in South Africa climbed over 0.6 percent, shrugging off data that showed private sector activity deteriorated slightly in January as output and new orders fell, while exports rose.
In emerging Europe, data showed manufacturing slowed in January for Europe's biggest post-communist countries, Hungary, Czech Republic and Poland, suggesting their economies are suffering from shrinking demand for their exports in the rest of the European Union.
Poland's central bank meeting was also watched: Officials are expected to keep rates on hold, although its currency was little changed against the euro.
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For RUSSIAN market report, see (Reporting by Agamoni Ghosh in Bengaluru; Additional reporting by Indradip Ghosh; Editing by William Maclean)