* Asian stock markets : https://tmsnrt.rs/2zpUAr4
* Nikkei rallies, hopes new PM will stick with stimulus
* China service PMI strong, blue chips highest since mid-2015
* Dollar near two-year trough as Fed commits to easy policy
* Risk of future inflation pushes up U.S. long-term yields
By Wayne Cole
SYDNEY, Aug 31 (Reuters) - Asian shares notched a 29-month high on Monday as investors wagered global central banks would keep topping up the policy punchbowl for years to come, while an upbeat reading on China's service sector augured well for recovery there.
MSCI's broadest index of Asia-Pacific shares outside Japan rose 0.2% to reach its highest since March 2018, bringing gains for the month so far to 5.1%.
Chinese blue chips firmed 0.7% to reach levels not seen since mid-2015, while the yuan hit its highest on the dollar in more than a year.
Surveys showed Chinese manufacturing activity edged back a tick to 51.0 in July, but services jumping a full point to 55.2 in a hopeful sign of reviving consumer demand.
E-Mini futures for the S&P 500 climbed another 0.4%, while EUROSTOXX 50 futures added 0.8%.
Tokyo's Nikkei rallied 1.6% aided by news Warren Buffett's Berkshire Hathaway had bought more than 5% stakes in each of the five leading Japanese trading companies.
The Nikkei had dipped on Friday after Prime Minister Shinzo Abe's resignation stirred doubts about future fiscal and monetary stimulus policies.
Those concerns were eased somewhat by news Chief Cabinet Secretary Yoshihide Suga, and a close ally of Abe, would join the race to succeed his boss. A slimmed-down leadership contest is likely around Sept. 14.
Attention was now on a host of Federal Reserve officials that are set to speak this week, kicking off with Vice Chair Richard Clarida later Monday as they put more flesh on the bank's new policy framework.
Fed Chair Jerome Powell boosted stock markets last week by committing to keep inflation at 2% on average, allowing prices to run hotter to balance periods when they undershot.
The risk of higher inflation in the future, assuming the Fed can get it there, was enough to push up longer-term Treasury yields and sharply steepen the yield curve.
Yields on 30-year bonds jumped almost 16 basis points last week and were last at 1.52%, 139 basis points above the two-year yield. The spread was now approaching the June gap of 146 basis points which was the largest since late 2017.
That shift was of little benefit to the U.S. dollar given the prospect of short rates staying super-low for longer, and the currency fell broadly.
Early Monday, the dollar index was off at 92.341 and just a whisker above the recent two-year low of 92.127. The euro stood at $1.1902, having climbed 0.9% last week.
Marshall Gittler, head of investment research at BDSwiss Group, noted speculators had already built up record levels of long positions in the euro which could work to limit further gains.
"A truly crowded trade that will take more news to push higher," he argued.
The dollar did steady a little on the yen at 105.60, after dropping 1.1% on Friday before finding support in the 105.10/20 zone.
In commodity markets, the weakness in the dollar helped underpin gold at $1,969 an ounce.
Oil prices steadied, having dipped on Friday after Hurricane Laura passed the heart of the U.S. oil industry without causing any widespread damage.
Brent crude futures rose 27 cents to $46.08 a barrel, while U.S. crude gained 14 cents to $43.11.
(Editing by Shri Navaratnam)