* Investors take profits after bullish bets hit record high
* Some worry demand may falter in Q4
* North Sea crude supply to fall in Nov (Updates with comment, refreshes prices; changes dateline from TOKYO)
LONDON, Oct 3 (Reuters) - Oil steadied on Tuesday, as speculators took profits on some large positions that have built up in the last couple of weeks, but the prospect of gradually ebbing oversupply lent support.
December Brent crude futures were virtually unchanged at $56.13 a barrel at 0851 GMT, having lost almost 2.5 percent on Monday. U.S. crude futures were down 2 cents at $50.56.
Brent notched up a third-quarter gain of about 20 percent, the biggest increase for that quarter since 2004, and traded as high as $59.49 last week, but has since fallen about 6 percent.
Money managers have pushed their bullish bets on the Brent crude market to a record high in the last week, encouraged by signs of rebalancing between supply and demand.
But when positioning becomes too stretched, this can lead to abrupt shifts in the price.
"It's always problematic when you have this amount of speculative length in the market," Petromatrix strategist Olivier Jakob said.
"The price action ... for me is all about positions and potentially profit-taking on some of those speculative positions."
Oil prices climbed last week on tension in Iraqi Kurdistan after the region's independence vote, with Turkey threatening to close a pipeline that brings oil from the region in northern Iraq to the Mediterranean.
Turkey has not carried out the threat, analysts said.
The recent rally had also been driven by signs that a three-year crude glut is easing, helped by a production-cutting deal among global producers led by OPEC.
However, Middle Eastern oil producers are concerned the price rise will stir U.S. shale producers into more drilling and push prices lower again. Key OPEC producers consider a price above $60 as encouraging too much shale output.
"The fourth quarter is not too kind to the price of oil, as we switch from summer demand to expectations of winter demand," said Jonathan Barratt, chief investment officer at Ayers Alliance in Sydney.
"A lot of (refinery) maintenance occurs at this time so feeder demand is not there."
Offering a small boost was the expected drop in supply next month of the four largest North Sea crude grades that underpin the dated Brent benchmark.
Output of Brent, Forties, Oseberg and Ekofisk will average 800,000 barrels per day (bpd) next month, down from 870,000 bpd in October, and down 10 percent year-on-year.
(Reporting by Amanda Cooper; Editing by Dale Hudson)