Islanders off the north west coast of Ireland will be the first people to vote on the fiscal treaty referendum, four days ahead of the rest of the county.
Ballot boxes will be shipped and flown off Donegal to Arranmore, Gola, Inishboffin, Inishfree and Tory Island to let more than 760 early voters have their say.
Gardai will collect the ballot boxes from the islands at the end of the day and escort them to Glenties Garda Station where the boxes will be kept in special storage until the count on Friday.
Just six people on Inishfree can cast a vote, with 25 on Gola, 64 on Inishboffin, 140 on Tory Island, and 530 people on Arranmore. Three recent opinion polls revealed a 60/40 split in favour of the European fiscal treaty among Irish voters when polls open nationwide on Thursday.
On Sunday night Taoiseach Enda Kenny appealed to the public and undecided to play a role in Ireland's recovery by voting yes In a televised address, Mr Kenny said people would make a decision that will have enormous implications for the country's future.
He claimed it would create stability in the eurozone, create the certainty and stability and give Ireland assess to emergency funds.
But Independent TD Shane Ross declared he would be advocating a No vote because he wants the referendum postponed or to be held a second time after any changes involving Greece, France and EU Summit are finalised.
Sinn Fein's Gerry Adams called on citizens to stand up for Ireland, be wise and reject "the failed policy of austerity".
As the Yes and No sides canvas for support over the next two days, more islanders will cast their votes.
Less than 200 people on Clare Island, Inishbiggle and Inishturk, all off Mayo, will go to the polls on Tuesday. And another 1,164 voters will vote on Inishmore, Inishmaan, Inisheer and Inishboffin, off Galway, on Wednesday. Islanders off the south west of Cork will vote when polling stations open nationwide on Thursday morning.