* Dollar index off 2-month peaks, on track for monthly gains
* European markets hit highs, then slip
* Investors keep an eye on weakening Chinese yuan
By Anirban Nag
LONDON, May 31 (Reuters) - Global shares steadied at one-month highs on Tuesday, on track for a third straight month of gain, while the dollar's recent rally to two-month peaks on expectations the U.S. interest rates could rise next month took a breather.
European shares fell, hit by a drop in Volkswagen VOWG_p.DE whose shares retreated after the German carmaker reported first-quarter earnings, although the region's stock markets were set for their best monthly performance since late 2015.
The pan-European STOXX 600 .STOXX and FTSEurofirst 300 .FTEU3 indexes were in the red, having hit peaks in early trade. The broader MSCI world equity index .MIWD00000PUS , was up a tad at 1,676.96 points, its highest since late April.
U.S. stock futures 1YMc1 ESc1 pointed to a firm start on Wall Street where trading will resume after the Memorial Day holiday. Earlier, Japan's Nikkei index .N225 ended 1 percent higher, extending a 1.4 percent rally in the previous day. It is up 3.4 percent for May, thanks to a subdued yen JPY= .
The dollar index .DXY , which tracks the greenback against a basket of six major currencies, was flat at 95.524, off a two-month high of 95.968 struck on Monday, but still on track for a 2.6 percent gain for the month -- its best in six months.
The dollar has risen recently on expectations of higher U.S. rates. Fed Chair Janet Yellen said on Friday that the central bank should hike rates "in the coming months" if economic growth picks up and the labour market continues to improve.
"The question for me here is whether the dollar can carry on rallying on the prospect of the Fed raising rates faster over the next 18 months than is priced in, as opposed to rallying only on expectations of a move in June or July," said Kit Juckes, macro strategist at Societe Generale (PA:SOGN).
Investors are awaiting key data this week before taking fresh positions. May's U.S. private-sector ISM manufacturing data, due on Wednesday, and non-farm payrolls report on Friday will be scrutinised and solid readings could further heighten expectations for a move as soon as the Federal Reserve's next policy meeting on June 14-15.
Economists predict the jobs report will show that U.S. employers added 170,000 jobs, slightly more than they did in April. Hourly wages are expected to show a 0.2 percent increase from the previous month. ECONUS
CHINESE YUAN EYED
Investors were also keeping an eye on the weakening Chinese yuan with worries about growth in the world's second-largest economy creeping back. The yuan was on track for its second largest monthly fall on record after the central bank softened its midpoint to a 5-year low. CNY/
"The prospect of higher U.S. interest rates will, in due course, test both the global markets and China's policy to manage its currency," said Jade Fu, investment manager at Heartwood Investment Management.
"In an environment of dollar strength, the People's Bank of China may well be forced to further depreciate the renminbi, risking the possibility of a one-off currency intervention."
In the commodities sphere, moves in crude oil futures were limited before Thursday's meeting of the Organization of the Petroleum Exporting Countries. Most analysts did not expect any changes in the group's flat-out production. was no Monday settlement for U.S. crude futures because of the Memorial Day holiday. They were up 0.5 percent at $49.58, lifted by the start of the peak demand summer driving season in the U.S.
Brent crude futures LCOc1 were lower at $49.36 a barrel, on rising output from the Middle East, but poised for a gain of nearly 3 percent for the month.
(additional reporting by Sudip Kar-Gupta and Jemima Kelly; Editing by Ralph Boulton)