Kingsbridge's Jobcentre Plus branch could be closed down as part of a review of employment services.
Centres in Sidmouth, Axminster, Exmouth, Okehampton, Plympton, Ilfracombe and Tavistock could also be closed under proposals unveiled by the Department for Work and Pensions.
Devon County Council and South Hams District Council have received letters from Phil Weeks, Devon and Cornwall District Manager for Jobcentre Plus, asking for their views on the plans.
The Department for Work and Pensions said the review was about ensuring local people receive the most efficient, cost effective services while taxpayers get the best value for money.
A spokesperson from the Department for Work and Pensions said: "Jobcentre Plus is currently reviewing the services it provides in its offices across Devon.
"This is to ensure local people receive the most efficient, cost-effective services while taxpayers get the best value for money.
"At this stage, local MPs, councillors and other stakeholders are being consulted on all available options and, before any final decision is made, all views will be taken into account."
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