After Elizabeth's death in 1712 he married secondly his first cousin the Honourable Elizabeth Annesley, daughter of Richard Annesley, 3rd Baron Altham, in 1737.
Richard Annesley, 3rd Baron Altham (1655–1701), Dean of Exeter and son of Arthur, 1st Earl of Anglesey
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Richard Annesley, 6th Earl of Anglesey (1693–1761), Irish peer, kidnapper and bigamist, son of the 3rd Baron Altham
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Richard Annesley, 2nd Earl Annesley (1745–1824), Irish politician and Member of the Irish Parliament