* Q3 price rally pushed Brent to mid-2015 highs
* Analysts say oil markets are largely rebalanced
* Say demand outlook leaves no room for increased production
* U.S. rig count suggests further rise in shale output
SINGAPORE, Oct 4 (Reuters) - Oil prices eased on Wednesday over caution that a price rally that lasted for most of the third quarter would not extend through the last three months of the year.
U.S. West Texas Intermediate (WTI) crude oil futures were trading at $50.05 per barrel at 0032 GMT, down 37 cents, or 0.7 percent, from their last close.
Brent crude futures, the international benchmark for oil prices, were down 35 cents, or 0.6 percent, at $55.65 a barrel.
Traders said the drops came over concerns that a third-quarter market rally that had lifted Brent to mid-2015 highs by late September had been overdone.
"Fundamentals may not yet be strong enough to support a continued rally, especially in growth-dependent commodities such as oil," said Ole Hansen, head of commodity strategy at Denmark's Saxo Bank in a quarterly outlook to investors.
Analysts say that a so-called market rebalancing is now well underway, meaning that demand is no longer undershooting available supply.
The re-balancing is a result of strong consumption and also due to efforts led by the Organization of the Petroleum Exporting Countries (OPEC) to cut output by around 1.8 million barrels per day (bpd) in 2017 and the first quarter of next year.
"Compliance with the OPEC production cuts was over 100 percent in August (meaning members produced less than their quotas, on average) and U.S. oil inventories have been declining for several months now," said William O'Loughlin, investment analyst at Australia's Rivkin Securities.
Preventing prices from climbing further, however, has been rising production in the United States, which is not participating in the deal to cut output.
U.S. production <C-OUT-T-EIA> hit 9.55 million bpd in late September, its highest level since July 2017 and not far off its 9.61 million bpd record from June 2015.
"The number of active drilling rigs in the U.S. increased last week, highlighting the fact that higher oil prices will inevitably lead to more production from U.S. shale. These factors have kept WTI oil in a relatively tight trading range for several months now," O'Loughlin wrote in a note to clients.
Drillers added six oil rigs looking for new production in the week to Sept. 29, bringing the total count up to 750, according to energy services firm Baker Hughes. <RIG-OL-USA-BHI>
Due largely to rising U.S. output, Saxo Bank's Hansen said that "an extension of output curbs beyond March (2018) will be needed to ensure continued support for the oil market".
(Reporting by Henning Gloystein; Editing by Joseph Radford)