Norhamshire or North Durham was an exclave of County Durham in England. It was first mentioned in 995, when it formed part of the lands of the priory at Lindisfarne, and was only abolished in 1844.

The district included the northernmost triangle of what is now Northumberland, with the exception of the area north of the River Tweed around Berwick-upon-Tweed. It was overseen from the village of Norham. Upon its abolition, the area became the Hundred of Norham.