GLOBAL MARKETS-U.S. stocks firm after debate but oil a drag

* Anxiety about Deutsche Bank (LSE: 0H7D.L - news) undercut post-U.S. debate gains

* Betting markets imply Clinton victory over Trump in debate

* Dollar gains, Mexican peso rebounds from record lows

* Oil prices recede on uncertainty over OPEC output talk

By Richard Leong

NEW YORK, Sept 27 (Reuters) - U.S. stock prices rose on Tuesday following the presidential debate between Hillary Clinton and Donald Trump, but losses in the oil market and anxiety about the fortune of Deutsche Bank limited Wall Street's advance.

Oil prices gave back some of Monday's gains on fizzling hopes of an agreement among major producers to freeze output in a bid to deal with the current global oversupply.

A stronger dollar in the aftermath of the first Clinton-Trump debate helped send gold prices lower.

U.S. and German government bond yields fell on safe-haven demand amid worries about Deutsche Bank and weaker oil prices.

"While the perceived debate winner or loser might have been a factor in early equity trading, the bond market is focused on other things, mainly concerns over certain banks, and their sustainability. Deutsche Bank is one of those banks," said Kevin Giddis, head of fixed income capital markets at Raymond James in Memphis.

Investors have fretted over Germany's largest lender in the wake of a massive $14-billion demand from the U.S. Department of Justice to settle claims on bad mortgage-backed securities.

Deutsche Bank wasn't the only European banks in the firing line. Shares (Berlin: DI6.BE - news) in UK-based Standard Chartered (HKSE: 2888.HK - news) fell over 3 percent on reports that it was facing a U.S. probe over an Indonesian investment.

Overseas equity markets initially rose as betting markets suggested Democrat Clinton won the first debate over Republican Trump, supporting the view of no radical changes in U.S. policies on the domestic economy, international trade and foreign policy.

Then Deutsche Bank shares drop to another record low at 10.18 euros led to a reversal in European stocks which spread to selling in other regions.

Europe's broad FTSEurofirst 300 index dropped 0.3 percent at 1,334.46.

On Wall Street, the Dow Jones industrial average was up 37.84 points, or 0.21 percent, to 18,132.67, the S&P 500 was 3.48 points, or 0.16 percent, higher at 2,149.58 and the Nasdaq Composite was up 21.76 points, or 0.41 percent, to 5,279.25.

The MSCI world equity index, which tracks shares in 45 nations, rose 0.74 points or 0.18 percent, to 416.94.

U.S. 10-year Treasury note yield slipped 2 basis points to 1.567 percent to its lowest level in over two weeks, while German two-year yield reached a near record low of -0.717 percent, according to Reuters data.

CRUDE PRICES RETREAT

Oil markets were also in flux as the world's largest producers gathered in Algeria to discuss ways to tackle a crude glut that has battered prices for two years now.

Brent crude was last down $1.26, or 2.66 percent, at $46.09 a barrel. U.S. crude was last down $1.25, or 2.72 percent, at $44.68 per barrel.

It was too early to determine whether Monday's presidential debate will result in sizeable changes among American voters for either Clinton or Trump in the Nov. 8th election, but the dollar, together with the Mexican peso and other higher-yielding currencies, enjoyed a bump.

The dollar index was up 0.4 percent at 95.649, while the Mexican peso gained 1.6 percent against the greenback.

Mexico's currency hovered near all-time low at 19.735 peso per U.S. dollar since last week on fears that a Trump presidency would threaten Mexico's exports to the United States, its single biggest market.

Spot gold prices fell $10.7501 or 0.80 percent, to $1,326.81 an ounce.

(Additional reporting by Marc Jones in London; Wayne Cole in Sydney; Editing by Catherine Evans and Nick Zieminski)