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Anne Scott, 1st Duchess of Buccleuch (11 February 1651–6 February 1732) was a wealthy Scottish peeress.

Anne was the daughter of Francis Scott, 2nd Earl of Buccleuch. In 1661, she succeeded to her sister's title of Countess of Buccleuch. On 20 April 1663, she married, James Scott, 1st Duke of Monmouth (the illegitimate son of Charles II of England his mistress, Lucy Walter) and she and her husband were created Duke and Duchess of Buccleuch on that day. They had seven children:

• Isabella Scott (d. 1748)
• Charles Scott, Earl of Doncaster (1672–1674), died in infancy.
• James Scott, Earl of Dalkeith (1674–1705), married Lady Henrietta Hyde, daughter of Laurence Hyde, 1st Earl of Rochester and had issue. {Laurence Hyde was the brother of Anne Hyde, Duchess of York-wife of James II of England}.
• Anne Scott (1675–1685), died young.
• Henry Scott, 1st Earl of Deloraine (1676–1730)
• Lord Francis Scott (1678–1679), died in infancy.
• Lady Charlotte Scott (b. & d. 1683), died in infancy.

The Duke of Monmouth was executed in 1685 following the failure of the Monmouth Rebellion, in which he attempted to win the English throne. The duchess married Charles Cornwallis, 3rd Baron Cornwallis on 6 May 1688, but they did not have any children. Anne died in 1732, aged 80 and her titles passed to her grandson, Francis.