From Tolkien Gateway

The East-mark was one of the three military divisions of Rohan, with the others being the West-mark, and the King's Lands around Edoras. The East-mark was defined as those lands that lay east of the Entwash and Snowbourn rivers. In military matters, the command of the Men of the East-mark would be given to one of Rohan's Marshals of the Riddermark. At the time of the War of the Ring this was the Third Marshal, the King's nephew Éomer, who held his command at the ancient township of Aldburg, the original capital of Rohan and the seat of his family.[1]

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