Sixty staff including about 30 nurses are to lose their jobs at North Devon Hospital in Barnstaple as the NHS Trust struggles to save money.
Northern Devon Healthcare Trust (NDHT) is facing debts of £7.9m and says that it has no other options.
It has already cut the use of agency nurses, reduced the use of bank staff and cut overtime.
The trust hopes to minimise the impact on staff through deployment and not filling vacancies.
'Not easy'
The trust, which employs 1,622 full-time staff in Barnstaple, will reveal details of how the cuts will affect staff over the next two months.
Spokeswoman Catherine Oliver said: "We are only too aware that this is a stressful and worrying time for staff and are committed to providing staff with the support they need.
"This decision was not an easy one to make, however, in this current financial climate we are under a great deal of pressure to review our working practices and so changes to the workforce are necessary."
Ken Terry, of health workers' union Unison, said industrial action could follow.
He said: "This is yet another example of the NHS in crisis.
"It appears that we receive daily information about trusts and their financial difficulties.
"Unison will oppose any compulsory redundancies by any means including industrial action."
The announcement is the latest of its type this year by NHS trusts which are making thousands of job cuts.
In March, Plymouth Hospitals NHS Trust announced about 200 job cuts to make savings of £22m.
In the same month, the Royal Cornwall Hospitals Trust, which is facing an £8.1m shortfall, announced it was to cut 300 staff.
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