Flankers Cudd, 26, and 27-year-old Evans have signed two-year extensions with the Rodney Parade-based region.
"I have no doubt that this news will give everyone involved with the Dragons a huge boost," said director of rugby Lyn Jones.
"Both Lewis and Nic are quality players. Lewis has characteristics that make him a really good leader."
Evans came through the Dragons age grades and played for Ebbw Vale and Newport RFC. before making his debut for the Men of Gwent in 2006.
Cudd has made 60 appearances for the region since joining from Llanelli in 2012.
Forwards Lewis Evans and Nic Cudd have agreed new contracts with Newport Gwent Dragons.