Walker, 21, is one step behind Paxton as both return from injuries that have them on the 15-day disabled list. Paxton will throw his second simulated game in Texas, expecting to throw three or four innings on Tuesday in conjunction with Walker.
Paxton on Saturday threw 36 pitches in his live session against Stefen Romero, Logan Morrison, Cole Gillespie and John Buck. Romero managed a broken-bat single in his first frame, while Gillespie hit a hard line shot back up the middle in the second. Romero later laced another base hit to right.
"It felt good," Paxton said. "I left some pitches over the middle, but overall no pain, and my stuff is feeling good. I'm making progress. I was probably throwing at about 85 percent. It's kind of hard to get that adrenaline going. But overall I felt great, and it's a good step forward."
Paxton was 2-0 with a 2.25 ERA in two games before he strained the lat muscle behind his left shoulder in Anaheim on April 8. If all goes well, he will head out on a Minor League rehab stint after another simulated game or two and could be ready to rejoin the Mariners' rotation around the end of May or early June.
Though not looking that far ahead, manager Lloyd McClendon said Paxton passed his first test against live hitters.
"It wasn't great, but it wasn't bad, and I suspect that he'll build on that," McClendon said of Saturday's session. "For his first time out [against live hitters], I thought he did OK."
Walker has yet to pitch in the Majors this year after dealing with a sore shoulder for most of spring, then getting shut down in mid-April after feeling some stiffness again during a Minor League rehab stint with Triple-A Tacoma.
The young right-hander, ranked the No. 5 prospect in baseball and No. 1 in the Mariners organization by MLB.com, said everything was sharp in the bullpen on Saturday except his cutter, which he will make a point of emphasis prior to facing live hitters Tuesday.
But overall, Walker said he felt stronger than he did in the similar leadup to his previous Minor League stint.
"I'm not getting tired in my bullpens," he said. "Today I threw 55, and that's a lot of pitches, but I got stronger at the end, so that was a plus. My arm strength is getting there."