Derry-born Republic of Ireland international Duffy arrived from Blackburn in 2016 while Dunk has made more than 200 appearances for the PremiDer League side,.
“I am delighted for both Shane and Lewis.” said manager Chris Hughton.
“They have been terrific players for the club, helping us win promotion and establish ourselves in the Premier League last season.”
Brighton beat West Ham 1-0 in the Premier League on Friday night 20:00 BST kick-off with a goal from Glenn Murray.
Hughton added: “Both Shane and Lewis are vital members of the squad, and it’s very pleasing that they’ve committed their long-term futures to the club.
“They have formed a very good central defensive partnership, and have played a really important role in what we’ve achieved.”