Some of my skins and mounted heads are being attacked by moths and some sort of bugs. I have tried spraying them with several types of insect killer. It seems to slow down the destruction but the bugs are coming back. I think they will destroy everything if some different action is not taken soon.
Any help would be appreciated

Sorry to hear. Hope you find a good solution!

I'm no expert, but I would suggest getting in touch with a taxidermist and/or a "pest control" company.

Maybe collect some specimens of the moths/bugs and get them to identify them. There are different methods for different species.

I do think freezing is an alternative for moths. But freezing can damage the mounts, so it need's to be done carefully.

You will probably also need to use some sort of pesticide. On the mounts and maybe also in part's of your room where insects might hide away.

This was just meant as a general advice, and the method will probably depend on what kind of insects you have. I would get "expert" help.

What Andres says plus on "horned " mammals the core,(inside the horn sheaths may not have been cleaned too good or at all. On antlered mammals if the skull plate wasn't cleaned correctly it turns into a breading ground for insects.
Seek out a "good" taxidermist in Ga to help you out,there are many. High price equals a "good" taxidermist. Don't go to a ham and egger guy.

Buy some Termidor and some Demon wp, and follow directions. The Demon will give a quick kill, and the Termidor will last for about a year.

Thanks guys I will try the Demon and Termidor also contact the taxidermist

do you have an exterminator who visits? We have one about once a month; he sprays all my skull mounts as well as his normal spraying in the house.

I had my taxidermist come and treat all of my mounts a few years ago, to include drilling holes in the horns of horned animals. Have not had a problem since.