The title is derived from the royal burgh of Roxburgh in the Scottish Borders that in 1460 the Scots captured and destroyed.

The Duke's eldest son bears the courtesy title of Marquess of Bowmont and Cessford.

The dukedom and its associated titles descend to heirs who shall inherit the earldom which in turn had a very specific line of descent.

The succession was originally to heirs male of the 1st Earl, but after his sons predeceased him, the title was recreated in 1646 with additional remainder in favour of "(i) his grandson by his eldest daughter, Sir William Drummond, and his issue in tail male, (ii) of his great-grandsons in like manner, i.e. the second and other younger sons of Jane Drummond, the sister of Sir William Drummond, by her husband John [Fleming], 3rd Earl of Wigtown [...] which failing (iii) of the eldest daughter of Hon Harry Ker, styled Lord Ker, without division and to her heirs male, which failing (iv) to his own heirs male whomsoever".

[citation needed] The current holder's son, Frederick Innes-Ker, Marquess of Bowmont and Cessford (born 2024) is heir apparent to his father's titles.