The Minister for Education is coming under increasing pressure to explain how education services will be delivered if the new Education and Skills Authority is not fully functional.
The Education and Skills Authority is due to be in place by the first of January to replace the five boards and the Council for Catholic maintained schools.
But the legislation to set up the new authority has not yet reached the Executive table.
The Chief Executive of the Belfast Board, David Cargo, has written to the Department of Education's Permanent Secretary warning that a meltdown of the service could take place.
The Chief Executive of the CCMS has also penned a letter to the Department saying that with no guarantee of when the new bill will be approved, he feels obliged to advise his staff to disengage from any activity associated with the establishment of the ESA.
"At the minute we are in the process of winding down CCMS. At the same time we have no legislation to start the new organisation, so there is some uncertainty and confusion", Donal Flanagan said.
"The biggest issue I have is in the absence of continuity planning, we could be putting the health and wellbeing of children at risk," he added.
UUP MLA and Education Spokesman Basil McCrea said: "It's about how you build consensus on the way forward.
"The problem with the Minister is that she will not engage with people to try and get quite sensible things resolved. All things are possible if you have dialogue and she's not engaging in dialogue".
Sinn Fein MLA and Education Spokesperson, John O'Dowd, said he believes progress can be made.
"The system is not in meltdown. I am not underestimating the difficulties faced by the boards and their managements and staff, transition is always a very difficult process. However I am confident that between the department, the boards and the new ESA team we will have a smooth transition".
Education Minister, Catriona Ruane, is expected to comment on the issue at a conference on Friday.
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