Jamie and Craig Overton have committed their futures to Somerset by signing contract extensions until the end of the 2018 season.
The 21-year-olds are highly regarded across the county circuit and both earned call-ups to the England squad for the one-day series against New Zealand, although neither made their debut for the Three Lions.
"Lewis, Craig and Jamie are outstanding cricketers with the potential to become even better," Maynard told the club's official website.
"They have all performed extremely well this year and have rightly received international recognition. We are very pleased to have secured their services because they will be an absolutely vital part of this club for the years to come.
"They are great lads who offer a lot both on and off the field."
The Overtons made their debut for the county in 2012.