DesmondTheFinch yeah, that sounds like he has scalyface mites, they're probably driving him crazy. It could be other things, such as a fungal infection or self-plucking from stress. The other male could also be plucking him. I can't say for sure, but it's probably mites if you've just got them recently.
You definitely should treat them with s.c.a.t, it's great for all kinds of mites including scalyface and airsac mites, and keeps them protected for a long time. You just put a drop on the backs of their necks and it kills any mites that come in contact with them.
You will have to treat both birds, as well as any other birds they may have come into contact with, and you will need a mite-killing spray for the cage as well or the mites will simply wait for the treatment to wear off, and new ones will breed.
2 black cheek zebras and 5 CFW zebras, one A&M pied coturnix hen, my darling cream/lavender coturnix roo, and his attitude.