The Environment Agency is warning of possible flooding on Friday morning, with heavy rain forecast overnight.
Flood alerts have been issued for the Rivers Clyst and Culm and their tributaries, in the areas of Broadclyst, Clyst St Mary, Stoke Canon, Cullompton and Hemyock.
Up to 35mm of rain is forecast for the early hours of Friday and heavy showers are likely to continue into the afternoon. The Environment Agency said this could result in river levels rising and an increase in surface water.
There are currently no flood warnings in force on the River Exe. Coastal and tidal areas between Plymouth and Lyme Regis are, however, subject to a flood alert, with overtopping and flooding possible as a result of strong winds and high water levels, expected to peak at 6am.