GLOBAL MARKETS-Stocks shaky as oil heads lower again

* Stock market mood sours slightly as oil bounce fades

* U.S. stocks to inch higher

* Promise of higher U.S. rates prods dollar higher

* Fed officials, Lagarde see lower fuel costs helping growth

By Patrick Graham

LONDON, Dec 2 (Reuters) - Stock markets wobbled in Europe after a strong start on Tuesday as oil prices resumed the sharp falls that have shocked global financial markets over the past month.

A bounce in oil prices on Monday from five-year lows had helped foster a broadly more positive tone in Asia, but by mid-morning in Europe Brent crude was down more than 1 percent on the day at below $72 a barrel. Oil has fallen more than a third since June.

Russia's rouble sank another 3 percent against the dollar while authorities in another major oil producer, Nigeria, intervened to prop up its naira currency.

"I am not surprised the (oil) price is going down. The market is looking for a renewed sense of direction and trying to figure out if we have hit the bottom or if we are about to go lower again," CMC Markets analyst Michael Hewson said.

The impact on stocks tied to energy was mixed, with some still higher on the day as investors priced in the impact of Monday's bounce in oil after Europe had closed for the day.

A 1 percent rise in London drove the pan-European FTSEurofirst index 0.5 percent higher but Germany's DAX index was flat and France's CAC up just 0.2 percent. U.S. stocks were set to open a touch higher.

The cancellation of Russia's planned South Stream gas pipeline to Europe drove shares in German steel pipe maker Salzgitter (Stuttgart: SZGA.SG - news) down 8.6 percent and Italian oil services group Saipem (Other OTC: SAPMY - news) 7.7 percent lower.

"The oil services sector has come down massively due to a lack of capex from the oil majors," said Caroline Vincent, European equities fund manager at Cavendish Asset Management.

"If you try and call the bottom to the sector now, it's too risky. It's like trying to catch a falling knife."

Behind the shock of the plunge in oil is a deeper debate about whether developed economies are slipping into a prolonged period of stagnation, or just coming out of the financial crises of the past five years more slowly than previously hoped.

IMF Managing Director Christine Lagarde said late on Monday that cheaper oil was a positive for the global economy. The drop has given a lift to travel companies and should have a positive impact on consumer spending.

"The weight of money does seem to want to come back into the stock markets and we're more likely to drift up going into the end of the year than to drift down," said Terry Torrison, managing director at Monaco-based McLaren Securities.

BONDS

European bond yields edged up, with strategists saying Monday's oil bounce had cooled speculation the European Central Bank could ease policy further this week as it seeks to revive euro zone growth.

Expectations the ECB and the Bank of Japan will print money next year are supporting stock markets bloated by the more than $4 trillion provided by the Federal Reserve since 2008.

"The urgent need for the ECB to act has disappeared in the background," said Emile Cardon, market strategist at Rabobank.

Fed Vice Chairman Stanley Fischer and New York Fed President William Dudley painted a mostly rosy picture on Monday, suggesting energy markets will not distract the U.S. central bank from lifting rates next year. That helped the dollar gain around 0.4 percent against a basket of currencies. (Additional reporting by Marius Zaharia, Sudip Kar-Gupta and Tricia Wright in London and Blaise Robinson in Paris; Editing by Catherine Evans)