Open appliance which has a flat round disk as a screw head, no recess at all
Those could be screws with the heads removed, specifically to prevent people from opening the device.  In that case, try to cut a slash across the top of the screw so that you can get a flat-head screwdriver in there.  A dremel comes to mind, although you'll damage the plastic casing, but, hey, if you want to make an omelette...

Just as likely though, they are like ring-shank nails, with notches on them designed to catch on the plastic inserts on the other side and ensure that they never, ever get removed without destroying the device.  In this case, the answer may be to drill the head off of them so that the shank can be pulled through the hole in the plastic.  Understanding, of course, that you won't be able to put them back together.  

Why do you want to take it apart, incidentally?