* U.S. crude stocks likely fell 3.4 mln bbls last week -poll
* OPEC oil output falls in Nov to lowest since May -survey
* Goldman, Morgan see oil continuing to strengthen
* API shows big crude draw, rise in gasoline, distillate stocks (Updates with API data, price reaction)
NEW YORK, Dec 5 (Reuters) - Oil rose on Tuesday, supported by strong demand, expectations of a drop in U.S. crude inventories and an OPEC-led deal to extend oil output cuts.
Faster-than-expected growth in demand this year has given tailwind to OPEC's efforts to clear the glut, and the latest U.S. inventory reports are likely to show a third straight weekly drop in crude stocks.
Analysts expect data on Wednesday from the U.S. Energy Information Administration (EIA) to show crude stocks fell 3.4 million barrels last week.
Industry group the American Petroleum Institute said late on Tuesday that crude stocks fell by 5.5 million barrels, more than expected. But gasoline stocks were up by 9.2 million barrels, and distillate inventories rose by 4.3 million barrels, far more than expected for both categories. The EIA and API numbers do not always run in tandem..
In quiet post-settlement trade, oil prices dropped. Brent crude settled up 41 cents, or 0.7 percent, at $62.86 a barrel while U.S. West Texas Intermediate crude ended 15 cents, or 0.3 percent, higher at $57.62 a barrel.
After the API data, U.S. crude fell to $57.48 a barrel as of 5:08 p.m. EST (2208 GMT).
Analysts looking to next year believe some tightening in supply will continue. Morgan Stanley analysts said in a note on Monday they expect demand to outpace supply in 2018, with most of the supply growth coming from the United States and Canada.
Goldman Sachs late on Monday raised its forecast for 2018 Brent and WTI to $62 and $57.50 a barrel, respectively, thanks to OPEC's resolve in maintaining production cuts.
The Organization of the Petroleum Exporting Countries, Russia and other non-OPEC producers last week extended the deal to cut output by 1.8 million barrels per day (bpd) until the end of 2018 to get rid of excess oil in storage.
OPEC has shown strong compliance with the supply cut pledge and in November output fell by 300,000 bpd to its lowest since May, according to a Reuters survey.
"Yesterday was defined by profit taking in post-OPEC trade," said Tony Headrick, energy market analyst at CHS Hedging LLC, adding that the market is now watching for further signals on what 2018 will look like.
The OPEC-led producer group's Nov. 30 decision to extend their supply-cutting deal could bolster U.S. shale drilling given overall higher prices.
Data last week showed U.S. crude output rose to nearly 9.5 million bpd in September, approaching the high of 9.63 million bpd seen in 2015. (Additional Reporting by Alex Lawler and Jane Chung; Editing by Marguerita Choy and Cynthia Osterman)