A rogue group of politicians are missing in action — and the police are hot on their trail.

It's an unlikely game of cat and mouse, but one that has found itself unfolding in the US state of Oregon, where 11 Republican senators have gone into hiding.

The political fugitives fled the State Capitol last week in order to deprive it of enough legislators to lawfully operate, in a bid to block a vote on a landmark climate plan.

The climate plan was expected to pass under the Democrat-controlled Senate (if you can't beat them, flee them).

But with things at a standstill until they return, state police have been deployed to track them down.

How did this happen?

A cap-and-trade climate plan is at the centre of the unusual stoush.

It aims to dramatically lower Oregon's greenhouse gas emissions by 2050 by encouraging businesses to switch to green technology — and unsurprisingly, it's not without controversy.

Some are concerned the climate proposal will lead to a spike in petrol and diesel prices. ( AP: Gillian Flaccus )

Minority Republicans are concerned the proposal will lead to a spike in petrol and diesel prices and want it to be sent to voters instead of being instituted by politicians.

But negotiations with Democrats, who have a clear Senate majority, collapsed last week, leading to the walkout.

This is important, because while the Democrats have an 18 to 12 majority in the chamber, there must be 20 members present for a quorum — meaning nothing can be done until at least two members return.

"It's time for the Senate Republicans to show up and do the job they were elected to do," Oregon Governor Kate Brown said.

What can the police actually do?

Governor Brown deployed officers to try to round up the rogue Republicans on Thursday.

Technically, Oregon State Police (OSP) can force any senators they track down into a patrol car and return them to the Capitol.

Expect things to be a little bit less gung-ho, however, with the agency preferring to opt for "polite communication" and patience instead.

"OSP will work with the Governor's office and members of the Legislature to find the most expeditious way to bring this matter to a peaceful and constructive conclusion," it said in a statement.

Oregon Governor Kate Brown deployed officers to round up the rogue politicians. ( AP: Andrew Selsky )

Kate Gillem, a spokeswoman for Senate Republicans, confirmed that some members had left the state to avoid a vote because police don't have jurisdiction outside Oregon.

The agency said it had been in contact with several senators and that officers were being assisted by "out of state resources".

Under state law, the absentee senators will be fined $US500 ($720) a day per person if enough of them remain absent to prevent a vote.

What have the politicians said?

The walkout brings all Senate business to a halt with less than a week left in the legislative session — and senators still need to vote on the budget.

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Unsurprisingly, Democrats aren't thrilled with the standstill.

"I beg and beseech my fellow legislators to come to the floor," Senate President Peter Courtney said.

"I need you, the legislature needs you, the people of Oregon need you to pass budgets to take care of our citizens."

But the Republican senators are sticking to their guns, concerned the cap-and-trade plan will exacerbate a growing divide between urban and rural Oregon.

"I'm not going to be a political prisoner in the state of Oregon. It's just that simple," Republican senator Brian Boquist told reporters during the walkout.

Senate Republican leader Herman Baertschiger added that the walkout "represents our constituency and exactly how we should be doing our job".

What happens now?

With the Oregon 11 unlikely to cede for now, and the closure of the Capitol over the weekend due to a "possible militia threat", the Senate has so far been unable to conduct business.

A group of local Republicans had threatened to protest inside the state legislature on Saturday (local time) when politicians were present, and anti-government groups said they could join, prompting the statehouse shutdown.

A poster made in support of the Republican politicians who walked out of the Capitol. ( Twitter: Tammy Bennett )

Right-wing groups have previously posted their support for the politicians on social media — in one instance offering to provide escorts to them should the state police come for them.

This is the second time in this legislative session that the minority politicians have used a walkout as a way to slow the process.

Democrats have a rare supermajority in Oregon's House and Senate, meaning Republicans don't have many ways to influence the debate.

The political adversaries were last month locked in a four-day standoff over a school funding tax package that only ended when the Governor struck a deal to table legislation on gun control and vaccine requirements.

ABC/AP