Northern Devon Healthcare NHS Trust and the Royal Devon and Exeter NHS Foundation Trust are to explore joining together ‘on a more formal basis’.
The boards of both trusts have agreed to the idea but say it must benefit the populations of both areas and be supported by NHS regulators.
As yet there are no details of what this 'formal joining' could mean if it goes ahead.
NDHT currently runs North Devon District Hospital plus community hospitals in South Molton, Bideford, Ilfracombe and Torrington.
RD&E manages a large teaching hospital as well as 12 community sites across East and Mid Devon.
Suzanne Tracey, joint chief executive of both trusts, said: "The starting point for both organisations is the clear view that wherever you live - whether that is in rural Northern Devon, in the centre of Exeter, or on the borders of Somerset and Cornwall - we have a shared duty, as part of the National Health Service, to ensure that people have good access to high quality care and, in particular, A&E and supporting services when they need them.
"We recognise that both organisations face some significant challenges. We both need to transform with the use of technology and recruit and retain the workforce needed to deliver high quality services to our patients.
"We both need to improve our performance against some of the key targets on accessing health services. We need to do this in a clinically and financially sustainable way.
"That is why we now need to explore whether working together on a more formal basis provides us with a better opportunity to address these challenges, making the best use of our collective resources to meet the health needs of the local population.
"Clearly, any new arrangement between the two organisations must be appropriately supported by NHS Improvement/NHS England."
The boards of both organisations say they will now work together to determine the next steps.
They have agreed that a Collaborative Agreement between them should be extended beyond June 2020 to allow the appropriate processes, including conversations with NHS regulators, to be completed.
The trusts say they are committed to 'keeping staff and the community informed and engaged' as this process develops.