Adam has signed a new two-year contract at the Banks's Stadium while twin brother James has extended his stay by a further year.
Saddlers boss Dean Smith said: "I'm really pleased they have both signed new deals. They are fantastic professionals and good people to have around the place."
Midfielder Adam joined Walsall two years ago and has proved a valuable member of the squad, making a total of 77 appearances, while he finished runner-up for the club's Player of the Year award last term.
"I'm very pleased to have signed this new deal," Adam said. "It's a situation that has been ongoing for a while, but I am glad it has been done and dusted now because I thoroughly enjoy it here and can concentrate on the season ahead.
"The club showed last season that we are moving in the right direction and hopefully that progress will continue."
Versatile full-back James, meanwhile, arrived last summer and went on to make 24 outings last term.
"It's a good club with good management and players," he added. "People saw what we were capable of during the second half of last season and hopefully we can recreate that form and push on from where we left off.
"From a personal point of view I feel that I was performing like myself towards the end of the season and now I can't wait for the new season to get underway."