* Nations attempt to strike U.N. deal to curb emissions
* China at odds with U.S. despite promises to cooperate
* Delegates seek deal that can adapt as warming shifts
By Environment Correspondent Alister Doyle
BONN, Germany, May 3 (Reuters) - New, more flexible ways to fight climate change were sketched out on Friday at the end of a week of talks between 160 nations, but there was no breakthrough in bridging a deep divide between China and the United States.
The meeting of senior officials in Bonn, Germany, aired formulas to resolve disputes between rich and poor on sharing out the burden of curbing greenhouse gas emissions as part of a new U.N. deal, a successor to the 1997 Kyoto Protocol.
Attempts to reach agreement have foundered above all on a failure to agree on the contribution developing countries should make to curbing the industrial emissions responsible for global warming. The next ministerial conference to try to reach a deal is scheduled for Paris in 2015.
The United States, recently overtaken by China as the world's biggest carbon polluter, never ratified Kyoto because it set no binding emissions cuts for rapidly growing economies such as China and India.
The United Nations said there was a broad agreement among delegates in Bonn that any new accord should have flexibility to ratchet up curbs on emissions, without a need for further negotiations, if scientific findings about floods, droughts and rising sea levels worsen in coming years.
That approach would be a big shift from the Kyoto Protocol, which binds about 35 industrialised nations to cut greenhouse gases, with targets set every few years.
"There's been quite a lot of common ground appearing," said Christiana Figueres, head of the U.N. Climate Change Secretariat. But she said no nation was doing enough to combat global warming.
"The agreement of 2015 cannot be cast in stone, cannot be frozen in time," she said of the idea of greater flexibility.
Some developed nations also suggested that a deal should have mechanisms, perhaps linked to per capita gross domestic product, so that governments in emerging nations would make bolder actions as their economies grew.
Governments agreed in 2010 to limit a rise in temperatures to no more than 2 Celsius (3.6 Fahrenheit) above pre-industrial times but are far off target. Economic slowdown has sapped many countries' willingness to act on climate change.
Temperatures have already risen about 0.8 C (1.4F) and many leading scientists say the 2C target is slipping out of reach. A U.N. panel says it is at least 90 percent certain that man-made greenhouse gases are the main cause of warming.
There were no breakthroughs in Bonn, with tougher decisions put off at least until a next session in June.
Developing nations said rich countries appeared unwilling to keep promises to take the lead in cutting emissions, and called for more focus on burden-sharing to safeguard the interests of the poor.
"If we fail to act now, a vastly more expensive response will be required later," a group of 83 of the least developed nations and small island states said in a statement.
China and the United States showed little indication of closer cooperation despite agreeing last month to step up efforts on climate change, saying they hoped that would inspire action by others.
China stuck to its insistence that developed nations should collectively cut greenhouse gas emissions by between 25 and 40 percent below 1990 levels by 2020. President Barack Obama's plan is the equivalent of a 4 percent cut.
The United States won some support for a suggestion that the 2015 deal should be based on national promises of action, while China wants far more binding commitments by the rich.
Chinese chief negotiator Su Wei also said China could not impose caps on its rising emissions because it needed time to focus on economic growth, despite U.S. calls for tougher action by Beijing.
"In China the per capita income is just around $5,000, compared to the industrialised countries where you have $40,000 or even more," he told Reuters. (Reporting By Alister Doyle, Environment Correspondent; Editing by Pravin Char)