How to hang Nelson clocks  

If you
can't pound your nail into a wood stud behind the sheetrock, use a sheetrock anchor which either screws into or opens behind the gyp board surface.
How large is the hole in the back of the clock ?

thank you
Thank you SDR. I was trying to hang it on drywall against the back of a fireplace. I had a sunflower clock hanging there for a couple yrs, and it did fine. This clock is smaller, but I am so scared that it might fall. Can I use the sheetrock screw on drywall against a fireplace? The screw hole is maybe an inch long? Looks like a keyhole. This clock is lighter than an asterisk clock, which I just hang on nails in drywall. Maybe I am over-reacting?

You might have masonry right...
You might have masonry right behind the drywall above you fireplace. (I do). Which is a good and bad thing. Good because it will be very solid once you've drilled a hole into it. Bad because you will need a hammer drill and masonry bit to drill the hole. And annoying because you may not have an air gap behind the drywall for a normal anchor to expand. But once you've got the hole drilled, a simple plastic plug with a screw in it will hold a lot of weight..
Otherwise, if it is empty behind the drywall, these anchors are great for extra heavy things where there is no stud:
http://t.homedepot.com/p/E-Z-Ancor-Twist-N-Lock-8-x-1-1-4-in-White-Nylon...