Floyd, who went on the disabled list twice in 2012 with elbow soreness, threw two scoreless innings, allowing two hits. The opposition was a true test as both pitchers had to toil against Team USA, which is warming up for the World Baseball Classic.
Thornton, who had been held back due to triceps soreness, pitched one inning. He threw 19 pitches and walked one in his scoreless frame.
Gavin Floyd made his spring debut against Team USA on Tuesday.
“I wasn’t really worried about the results,” Thornton said. “I wanted to go out and throw some breaking balls and some changeups. I fell behind on the count a couple of times, but I felt great. That is all I am worried about.”
Floyd will throw a side session in a couple of days and start again in five days. Thornton has mapped out a schedule with pitching coach Don Cooper and the training staff.
“We are going to throw a sideline when we get back from the off day (Wednesday), then I will throw in a game on Saturday,” Thornton said.
The White Sox hope a solid pitching staff can help them contend in 2013. Early injuries to Thornton and veteran right-hander Jesse Crain have some Sox officials concerned about the wear and tear on the bullpen with only 26 days left until opening day.
“Jesse is going to be fine,” Thornton said. “It was something minor and they shut it down early. That will not be a major problem for him. The addition of Matt Lindstrom and Nate Jones establishing himself --he will be a go-to guy for us. We are going to be in a good place and I am looking forward to it.”
Thornton has been the most durable pitcher in baseball since coming to the Sox in a trade before the 2006 season. His 472 appearances are the most in the American League over the past seven seasons.