Residents of three groups of remote Scottish islands, some of which straddle oil and gas fields northeast of Britain, are calling for their own breakaway votes and greater autonomy.
Islanders from Shetland, Orkney and the Western Isles have lodged a petition with the Scottish parliament asking for a vote on 25 September.
That vote would come a week after a referendum on whether Scotland should end its ties with the United Kingdom after 307 years.
Local councils in the three island groups have also launched a campaign called "Our Islands, Our Future" to seek more powers after the 18 September vote, whatever the result.
New powers could include control of the sea bed around the islands.
The moves follow debate over the powers that Shetland and Orkney would have if Scotland became independent, with local officials saying that around 67% of North Sea reserves lie within their coastal waters.
Nationalists argue Scotland can be a prosperous nation with oil money to offset its relatively higher state spending and forecasts of oil and gas revenue of between £31bn and £57bn between 2012-2013 to 2017-2018.
But islanders, wary of governments in both London and Edinburgh that they accuse of ignoring their needs, are keen to control their own resources.
Tavish Scott, Shetland's representative in the devolved Scottish parliament, said Scotland does not have an economy without oil and gas, giving Shetland some leverage.
"We want to make sure that out of this big constitutional debate, we decide what we want for our future, because Edinburgh doesn't tend to pay much attention to the islands," Mr Scott told reporters today.
The islands' call for more power comes as the campaigns over Scottish independence gather pace, with separatists still trailing in opinion polls but gaining ground.
An ICM poll published yesterday was the second survey in a week to show the pro-independence movement catching up, with 39% of 1,010 people questioned in favour of independence, up two percentage points from a month ago, while the No vote dropped to 46% from 49%.
The undecided voters were 15%, down one point.
The petition calls for three separate referendums for people of each island group to let them vote on whether they should become independent, stay in Scotland, or, in the event of a Yes vote in September, stick with the United Kingdom.
The petitioners said the three island groups were culturally very different but shared some common history.
Orkney and Shetland, with populations of about 21,000 and 23,000 respectively, were under Norwegian rule from the ninth century until 1472.
The Western Isles, also known as the Outer Hebrides that lie off western Scotland, are home to about 27,000 people with the picturesque island chain a popular tourist destination.
A spokeswoman for the Scottish parliament said more than 620 people had signed the petition since it opened for signatures on 20 March.
It closes on 28 April, when a parliamentary petitions committee will decide how to proceed with the request.
"This is a quite a large number in a few days so it is clearly generating a lot of interest," said the spokeswoman, adding that there was no particular number of signatures needed to ensure the petition went before the committee.
But whether the petition leads to an independence vote or not, island authorities, who currently have some powers such as collecting property tax and education, see political change in Scotland as a time to make sure their needs are considered.
"This is a once in a lifetime moment to do something really special for island communities like ours," said Orkney Islands Council Convener Steven Heddle in a statement.