Cordero, 26, will have surgery in California Tuesday with Dr. Lewis Yocum performing the operation. Dukes, 24, is scheduled for arthroscopic knee surgery on Wednesday in Tampa, Fla., with Dr. Koco Eaton performing the procedure.
Cordero is expected to be sidelined for 9-to-12 months recovering from a torn right labrum while Dukes is expected to be out until late August or early September.
Cordero appeared in just six games this season. He had a 2.08 earned run average with no saves. In 305 career games, all with the Washington/Montreal franchise, Cordero has a record of 20-14 with a 2.78 ERA and 128 saves.
Dukes is batting .263 with six home runs and 20 RBI this season. In 104 career games with Tampa and Washington, Dukes is hitting .226 with 16 home runs and 41 RBI.