A letter from the council's chief executive Mike Mansell was sent to staff last week.
In the letter Mr Mansell says the authority has done "fantastically well" in saving close to £2 million over the past three years.
But he warns that a similar sum must be saved in the coming three years and says compulsory redundancies cannot be ruled out.
In the letter he says: "North Devon Council has tried to avoid or at least mitigate against the amount of job losses by cutting back on other things such as the lease car scheme and mobile phones.
He adds: "Unfortunately compulsory redundancies cannot be ruled out, however the council will do its utmost to avoid this."
Staff are asked to consider a number of ways they could change their working arrangements. Options include:
- a reduction in the number of hours they work
- unpaid leave for a fixed period
- early retirement on the grounds of efficiency
- voluntary redundancy
- any other opportunities they want to explore.
Staff have until November 23 to apply to change their working arrangements. The council's senior management team will consider the applications in December.
The council said today: "There is nothing unusual about this letter. It is the third time we have sent it out to staff and it usually goes out at this time of year. Each time it has gone out we have made significant savings from voluntary arrangements."