iMac Powering On - On its own

Has anyone heard or had this problem.
It started happening few nights ago, I use to put my iMac to sleep at night. And it started waking up, I assumed some how the desk must've gotten nudged. So I turned it off Wednesday night before I went to bed, woke up 12.40 and it was powered on, to the login screen. And again last night, I powered it off before I went to bed and this time i was awake when it happend, it powered on again by itself.
I don't have an exact time, except for last night it was 12.01, the other nights I believe I always saw it on after 12.
Is there some sort of clocking issue or anything like that?
It's a 20in G5 (the one that came out with the iSight camera, before the intel cores).

Not sure why but mine (17" G5) does this as well. I was sleeping on my futon one night and randomly heard the gong and saw it turning on. I haven't bothered to look into getting it fixed since I am at school and the computer works fine but since I am still under applecare I will probably get it checked out when I am home in the winter