International talks on climate change, and other subjects, follow an iron rule, according to Margaret Beckett, formerly foreign secretary and environment secretary of the UK, and a veteran of many late-night international negotiating sessions.

First, she says, there is false euphoria as negotiators appear to be eager for an agreement. This is followed by an inevitable period of false despair, as the wave of high expectations breaks against the rocks of countries’ entrenched positions. Finally, after several ups and downs, the rollercoaster of the negotiations settles into a compromise agreement – if the participants are lucky.

The long-running United Nations negotiations on a new framework for cutting global greenhouse gases have followed the rollercoaster rule faithfully, and many times over, in the past few months – a pattern that is likely to continue until the final stages of the summit in Copenhagen in December.

The purpose of the Copenhagen conference is to forge a binding international agreement that will oblige countries to cut or curb the growth of their emissions, in the hope of ensuring that global temperatures do not rise by more than two degrees Celsius over pre-industrial levels. Beyond that temperature, scientists predict, many of the effects of climate change – droughts, floods, heatwaves, storms – are likely to become catastrophic and irreversible.

There is already such an agreement – the Kyoto protocol, signed in 1997, which requires developed countries to cut their emissions by about 5 per cent on average, compared with 1990 levels, by 2012. But that pact was a failure, because the US refused to ratify it and developing countries took on no commitments on curbing their greenhouse gas emissions. In any case, the main provisions of the protocol expire in 2012, and if there is nothing to replace them the world will be left without an international instrument governing greenhouse gases.

What countries are hoping to agree at Copenhagen will not be a fully articulated international treaty in the mould of Kyoto. That must wait until next year, as there is not enough time for it to be fully worked out in December.

Instead, they want to sign a binding agreement on four key points, the details of which will have to be worked out later. The four elements, as identified by the United Nations, are: developed countries to take on emissions-cutting targets for the medium term, generally defined as 2020; emerging economies will not have to pledge absolute cuts, but will have to commit to certain actions to curb the future growth of their emissions; financial assistance from rich nations to developing countries, to help them lower emissions and adapt to the effects of warming; and institutions to be set up that will govern the above.

A political agreement on all of the key elements is “doable”, insists Ed Miliband, the UK’s secretary of state for energy and climate change. His optimism is echoed by other key players, including Yvo de Boer, the UN’s top climate change official, and Todd Stern, the US special envoy for climate change, who says: “There is a deal there to be done.”

But the negotiators also agree that getting to a deal in the time available will be tough. Although there has been distinct progress on several of the issues, problems remain.

Most rich countries have set targets to cut their emissions by 2020 – for instance, the European Union has agreed a 20 per cent cut from 1990 levels, rising to 30 per cent if other countries agree, and Japan has set 25 per cent as its target. But the US, the world’s biggest economy and second biggest emitter, has not yet done so.

The problem for the US is that its targets are contained in a bill currently before the Senate. That bill, which would put in place a system to cap emissions from industry and issue companies with tradeable permits to produce carbon, would set a target of 20 per cent reductions in emissions by 2020 compared with 2005 levels. But the passage of the bill is by no means guaranteed, and the US runs the risk of appearing to pre-empt Congress if it agrees a target at Copenhagen ahead of time.

The US may also find it difficult to name the sum that it would be prepared to contribute to poor countries, for the same reason.

Financing is proving troublesome for other countries, too. The sums proposed by players such as the EU have been derided as insufficient. Developing countries are threatening to refuse to sign up to any agreement unless adequate financing is assured, and this will take the negotiations down to the wire. Financing “will be the last thing” that is agreed, says Mr Miliband.

Financing is not the only bone of contention, though it is the biggest. Developing countries also say the rich world is not ambitious enough in its emissions-cutting targets, and most have not yet agreed to take on legally binding commitments to curb the future growth of their emissions that rich countries are demanding. There is also disagreement over the legal form an agreement would take, especially whether it would retain the structure of the Kyoto protocol or dispense with it in favour of a wholly new treaty.

At present, with six weeks to go before the talks finish on December 18, there is no way of telling whether Copenhagen will produce agreement on the key issues, or whether the talks will break down and have to be continued next year. There are plenty of ups and downs left before the rollercoaster comes to a stop.