Health Minister Stephen Donnelly says a number of health services should be back up and running in a number of days but it will be several weeks before they all resume.
Radiology, oncology and maternity services are among those being prioritised.
The General Manager of Letterkenny University Hospital says no timeline for a full restoration of services at the hospital is available at this stage.
Sean Murphy told the Nine til Noon Show that while progress is being made it is very slow:
