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.

Maenclochog Community Council currently pays about £3,000 a year to maintain the small toilet block in the village.
Residents have decided to hold a public vote throughout August on whether they should continue to do so.
Nine community councils and groups currently pay for the running costs of public toilets in Pembrokeshire.
Thirteen have closed in the county in the past few years as Pembrokeshire council aims to save money.
Eifion Evans runs one of the shops in the village.
He said: "It's a good idea because we can find out how many people want to keep the toilets going.
"There was uproar in the village when it was originally suggested they might close."
The toilets are popular with walkers who visit the nearby Preseli Hills.
Councillor Huw George, a member of the council, said its share of council tax "doesn't allow for the payment of these toilets at the moment".
But he added: "One possible way forward could be to add £7 or £10 a year to the annual precept."

The world number seven will feature alongside seven other players, including Maria Sharapova.
All matches in the event, which begins with a round-robin stage, comprise a single tie-break to 10 points.
"Tie-breaks provide so many pressure-filled moments and it will be fascinating to see who handles it best," said Konta, 25.
The winner of the inaugural women's tournament will receive $200,000 (£161,000), with an additional $100,000 (£80,547) donated to a charity working to combat domestic violence.
The men's tournament, which features US Open champion Stan Wawrinka and world number seven Kei Nishikori, runs alongside the women's event.
Britain's Andy Murray has reached the final of the past two events, losing to compatriot Kyle Edmund in London, and Austria's Dominic Thiem in Vienna.

Ipswich Town left back Tyrone Mings, 22, published a text message exchange between him and his mother on his Instagram account.
His mother thanked him for wiping "all my debt away", with Mings replying she deserved "every penny" and saying: "This is why I do it."
A club spokesman said it was a "private matter between Tyrone and his mum".
The player won praise on the social networking site, with one person calling him a "hero" and someone "who all children should look up to and aspire to become".
It is not the first time the footballer has expressed his generosity.
Last July, Mings offered via Twitter to buy new shirts for fans who had his old squad number stamped on their new kits.
Four months previously, he gave  two match tickets to a fan after he complained he had no money.
Mings, who comes from Bath, joined Ipswich Town in 2013 after the manager saw him play for just an hour with non-league side Chippenham Town.
He has been linked with a big money move to Premier League giants Arsenal.
Forwards Lewis Evans and Nic Cudd have agreed new contracts with Newport Gwent Dragons.
[NEXT_CONCEPT]
People living in a north Pembrokeshire village are being asked to decide on the future of their public toilets.
[NEXT_CONCEPT]
British number one Johanna Konta will play in the first women's Tie Break Tens event, in Madrid on 4 May.
[NEXT_CONCEPT]
A footballer who has become known for "great gestures" has now seemingly paid off his mother's debts.