Polling stations open at 7am and will close this evening at 10pm.
Nationally referendums rarely get above a 50% turn-out.
Voters on Donegal’s five inhabited islands have already voted on Monday last and those votes are under lock-and-key at Glenties Garda station.
Voters at dozens of polling stations in Donegal may also encounter silent vigils which have been organised by a Catholic priest and his Church of Ireland counterpart.
Father John Joe Duffy from Arranmore Island and Rev John Deane from Ardara have come together to protest at cuts in education.
Counting of the votes begins at 9am tomorrow and a result in the referendum is expected tomorrow afternoon.