The ASTI says it has a number of serious concerns over the decision to postpone the Leaving Cert exams until late July or early August.
The Education Minister announced yesterday that the Leaving Cert will now begin in either late July or early August.
The Junior Cert exams have been cancelled, to be replaced with in-class assessments at the start of the next school year.
However, after consultation with its Standing Committee last night, it is welcoming, in principle, the news the Leaving Cert exams will go ahead.
The ASTI's Kieran Christy said they have concerns about the change to the Leaving Cert.
"They relate to special needs provisions, the need for social spacing, practical examinations and the requirement for people to finish project work that lies in school classrooms currently and is inaccessible."
The Irish Second Level Students Union says there are still a lot of unanswered questions surrounding the state exams taking place in the summer.
Minister McHugh has says he hopes sixth year students will have two weeks in class before the exams start.
Sean Carey, from the secondary school students union, says there needs to be more clarity.
"We have major concerns regarding transition from second level to third level, the mental health impact that the stress and anxiety is going to have on students over the next few weeks and what kind of assessment is actually going to take place," said Mr Carey.
"They have given us a rough outline of times but there is no clear deadline.
"A lot of students are really wondering whether or not they are going to be going back to school.
"We are glad to have some clarity but also disappointed in a lot of regards."