The Irish Second-Level Students Union is calling for the standard Leaving and Junior certs to be scrapped this year.
It has written to Education Minister Norma Foley, calling for an alternative format for 2021.
Schools are closed until at least January 31st - but the Minister says she intends to run the exams as planned in June.
But Reuban Murray, the union's president, says that's not practical.
"In terms of the Leaving Cert, we need to recognise that the exams as we thought they would happen before Christmas cannot go ahead as planned.
"We need the Department of Education, ourselves the students, all the stakeholders, to sit together and talk.
"What are our different options for an alternative Leaving Cert? And the Junior Cert as well, because we cannot forget the early school leavers, where the Junior Cert is their only qualification."
