Right-handed closer Ryan Madson has begun throwing again while left-handed reliever Sean Burnett is likely a week away from throwing.
Scioscia said Madson is playing catch, his first throwing action since Feb. 1 when he felt soreness in his surgically repaired throwing elbow that caused him to miss all of last season. He is coming back from elbow ligament-replacement surgery.
Burnett, who signed a two-year, $8 million contract during the offseason, aggravated his lower back while lifting his child into a car last week.
Scioscia said Burnett could begin throwing within a week.
"He feels better," Scioscia said. "He's day to day. We expect to see him next week and get evaluated and we'll see when he can start throwing. We don't have a prognosis on that. It might come a little quicker, I don't know."
Both pitchers were brought in to upgrade an area of need.
The Angels' 38 saves were four below the American League average last season and only four teams finished with a lower total. Their 22 blown saves tied Boston for the league lead.
The Angels bullpen's collective 3.97 ERA was third from the bottom in the American League.
Madson, 32, was brought in specifically to close out games and was signed to a one-year, $3.5 million contract.
"He's playing catch," Scioscia said.
The Angels did not expect Madson to be ready by opening day, but Scioscia said earlier in camp that he would be ready by sometime in April.