It's a wood fiberboard that was usually used as a non-structural sheathing often with an outer surface weather resistent treatment like asphalt, etc. Rarely it was used on the inside in place of plaster or drywall as well since it isn't very strong and can warp. It was commonly called beaverboard, blackboard, grayboard, or buffaloboard and was made by Celotex, Homasote, International Bildrite, Georgia Pacific, Knight Celotex, and Temple Inland.

I can't tell you anything more without knowing the design of the wall and the climate.

Macv,
Thanks for the response. I'm a total novice & just learned the name of this material.This is used inside and is covered by the wallpaper & paint. It is nailed directly to the studs-I can see the nail outlines through the falling off wallpaper. Right now I have more pressing problems such as the house sliding down a hill so the interior will have to wait. I was just pleased to know what the stuff was called!
Susan

Can you paint this stuff. it's all over my house/

Mine's painted ... all over my house too. I actually like it. I find it has a far more interesting texture than plain old drywall.