Jacobite succession (since the deposition of James II and VII in 1688) would support the Stuart pretenders' claims, of whom were James II & VII and Charles Edward Stuart, amongst others.
The Jacobite succession is the line through which Jacobites believed that the crowns of England, Scotland, and Ireland should have descended, applying primogeniture, since the deposition of James II and VII in 1688 and his death in 1701. James's son, James Francis Edward Stuart (the 'Old Pretender') and his grandson Charles Edward Stuart (the 'Young Pretender', 'Bonnie Prince Charlie') actively participated in uprisings and invasions in support of their claim. 
