Royals was the first to go down, suffering a right knee sprain on July 31 when he was run into by one of his teammates during a punt drill.
Alstott was sidelined on August 3, when he strained a hamstring during practice.
Alstott and Royals practiced for the first time since suffering their injuries. Tampa Bay's training camp has ended, so the Buccaneers are holding practices at One Buccaneer Place.
Alstott participated in individual drills for about one hour on Tuesday afternoon. The A-Train will not likely play against New England this Saturday night at Raymond James Stadium, but should be able to play in the Bucs' preseason finally at Atlanta on August 31.
Royals punted throughout the afternoon on Tuesday, but he is also not expected to play against New England.
In other injury news, LB Marq Cerqua (shoulder dislocation), G Russ Hochstein (broken foot) and DE Marcus Jones (hamstring) did not practice on Tuesday.
Subscribe to Buccaneer Magazine today by calling 1-800-881-BUCS(2827).