The Environment Agency has put out the alerts - the first stage in its warning system - as heavy rain falls in the region.
A spokesman advised residents to keep a ‘close eye’ on the weather forecast.
In Sheffield the Rivers Sheaf and Don, Blackburn Brook and the Porter Brook, all have alerts.
The rivers Rother in Rotherham and the Dearne in Mexborough, plus Rother and Doe Lea in Chesterfield and Staveley, Derbyshire, are also affected.
Visit www.environmentagency.org.uk for updates.
Call 0845 988 1188 to report flooding.