Hi guys! I’m making a game in which my main character has a walk cycle, a run cycle and a punch animation. I need him to be able to punch while he’s walking or running, but I don’t know how to combine the animations, i.e., make the walk or run cycle continue even while the punch animation is playing. I’d appreciate any advice. Thanks!
We have no idea how you made your animations - no images - no blend file. So we cannot help you unless we see how you got to where you are now. in theory it is perfectly possible to add a punch animation that effects the upper body to a walk cycle by just making the punching man walk as well, but I cannot begin to guess how you did yours so… images and/or blend files please!
Cheers, Clock. 
Oops, sorry! Here are two screenshots.
This one is the punch animation, with keyframes only on the right arm.
And this one is the walk cycle, with keyframes on just about every bone in the bear’s body.
At the bottom of both pictures, you can see the logic bricks for the armature. If you need a better picture of that, just let me know.