Is this the same as Final Fight 3? If so, the whole soundtrack was composed by Katsunari Kitajima. I can't remember where this info was unearthed, I think it was a personal website. It's just my hypothesis, but it seems like towards the end of the SNES cycle, Capcom started to contract outside composers and moved their main guys to arcade.
Edit:
http://www.dflat.jp/About.html