According to Rays manager Kevin Cash, Rasmus and Duffy both had good days on Tuesday while taking part in workouts at Tropicana Field.
"Encouraging news that they're recovering and feeling good during their rehab and their drills on the field," Cash said.
Both were expected to work out again on Wednesday.
Duffy, who is recovering from left heel surgery, will begin the final leg of his rehab once he's able to run. He said last week that he expects to run once the team returns from the current road trip. That would see Duffy do so at Tropicana Field next Tuesday if all goes well.
"Don't know [if he'll run then]," Cash said. "We're [five] days away. Hopefully he is, but if he isn't [ready], it isn't the end of the world."
In Duffy's absence, Tim Beckham has been playing shortstop.
Rasmus, who has been recovering from October hip surgery, had been on a rehab assignment at Class A Charlotte. He got banged up Thursday during an outfield collision. Rasmus told reporters earlier in the week that he is "day to day."
Rasmus will primarily play left field once he returns. Currently the position has been occupied by Mallex Smith, Peter Bourjos and Corey Dickerson.
Meanwhile, Boxberger (right flexor strain) has advanced to where he can take part in sock drills. The drill sees the pitcher put a sanitary sock with a baseball inside of it. He then throws the ball with the ball still in the sock.
Bill Chastain has covered the Rays for MLB.com since 2005. This story was not subject to the approval of Major League Baseball or its clubs.