ePSXe does work with WinME. I've got Win98SE on my machine once again though. Soon to be XP, just have to wait and see if my other most used progs work fine for it or not.
Anyway, I used to have WinME on my system and ran ePSXe just fine. The only reason its off my system now is some very odd packet handling in Everquest, that I hadn't noticed with Win98SE. So I went through the process of baking up & formatting my hard drive, only to find out that I had the same problem in Win98SE and it was infact my NIC that was causing the problem.
Well, that was background story that wasn't needed, but just to reiterate, ePSXe worked fine for me in WinME with an 800 T-Bird, 512MB Ram, Radeon 64 & SB Live! And it works just the same now as it did then. I'm hoping it will in XP too and from what I've been reading it seems it will...