Businessman and former dancer Michael Flatley and former weather presenter and meteorologist Joanna Donnelly have both withdrawn from the Presidential Election race.
In a post on Facebook, Mr Flatley said he is "honoured by the encouragement and support" he has received from "so many people across Ireland over recent weeks, but I must put my family and my health first".
"I feel I can better serve the Irish people by continuing my work promoting Ireland and Irish culture globally."
In a post on Instagram, Ms Donnelly said: "While I still believe that I have the qualities that would make me a good Uachtarán na hÉireann, I was naive to think I could meet the challenges of the campaign."
"Therefore, at this stage, I've decided it's best to withdraw my request for nominations."
Ms Donnelly, who left Met Éireann unexpectedly in April, confirmed on Tuesday that she was seeking a nomination.
She said she had not been approached by any political party to contest the election.
However, Ms Donnelly said that since then she has been speaking with people with "vastly more experience in this type of campaign".
"I've come to see just how wholly unprepared I am," she added.
She thanked the public for their comments of "support and encouragement".
Meanwhile, four independent candidates seeking to run in the presidential election are to be invited to a selection caucus in Leinster House next Thursday.
The caucus is being organised by Aontú Leader Peadar Tóibín.
Mr Tóibin said he hopes it will result in one of the four securing a nomination.
