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UPDATE 2-Oil markets stable, but doubts over recent bull run emerge

* Brent crude futures have risen over 40 pct since July

* OPEC-lead supply cuts have been main price driver

* Record U.S. output undermines efforts to tighten market

* China import growth slowdown also surprised market (Adds Texas drilling permits, updates prices)

SINGAPORE, Nov 9 (Reuters) - Oil prices held steady on Thursday after falling late in the previous session, supported by ongoing supply cuts led by OPEC and Russia.

However, traders said a price rally that has pushed up Brent crude by over 40 percent since July may have run its course due to increases in U.S. supplies and some indicators of a demand slowdown.

Brent futures were at $63.58 per barrel at 0516 GMT, up 9 cents, or 0.1 percent, from their last close, but over $1 off the more than two-year high of $64.65 reached earlier this week.

U.S. West Texas Intermediate (WTI) crude was at $56.87 per barrel, up 6 cents, or 0.1 percent, but also some way off this week's more than two-year high of $57.69 a barrel.

Key support was coming from efforts led by the Organization of the Petroleum Exporting Countries (OPEC) and Russia to withhold supplies in order to tighten the market and prop up prices.

OPEC will discuss output policy during a meeting on Nov. 30, and it is expected the group will extend the current cuts beyond their expiry in March 2018.

"With the OPEC/non-OPEC deal extension beyond March 2018 a certainty, prices may become stronger and temporarily reach the $65-$70 per barrel range in 2018," said energy consultancy FGE.

Despite this, many analysts say the strong price rally of the past months has likely run its course, at least for now.

U.S. crude stockpiles <C-STK-T-EIA> rose 2.2 million barrels in the week to Nov. 3, to 457.14 million barrels, the Energy Information Administration said on Wednesday, contrary to analysts' expectations for a decrease of 2.9 million barrels.

U.S. crude production <C-OUT-T-EIA> inched up 67,000 barrels per day (bpd) to 9.62 million bpd, the highest on record.

And output is set to rise further. Texas issued 997 oil and gas drilling permits last month, up nearly 17 percent versus the same month a year ago, the state's energy regulator said on Wednesday.

On the demand side, global oil demand remains strong, although the latest figures from top importer China came in below expectations.

"At 7.34 million bpd, China crude oil imports dipped to the lowest level since October last year... The trend could continue for the rest of the year," Barclays bank said, although it added that it expected demand growth to pick up again in 2018.

Key for the last weeks of the year is whether traders remain confident about their huge bets on further price rises, or whether they sell out of these positions, satisfied with recent strong gains.

"It doesn't matter how bullish the fundamentals are ... when an asset goes vertical there is always room for a pullback and consolidation of recent price moves. That's where oil prices find themselves this morning," said Greg McKenna, chief market strategist at futures brokerage AxiTrader.

(Reporting by Henning Gloystein; Editing by Richard Pullin and Christian Schmollinger)