You should try to separate the concerns between the web application and the class libraries. The class libraries should have as little knowledge as possible about the fact that a web application is calling them. In particular, they should not be using Session state or Application state. In fact, they should preferably have no reference to System.Web.dll!
Have the web application pass to the class library the pieces of Application state that the class library needs. The class library should have no knowledge of the fact that the data came from Application state.
This will also make it much easier to unit test the class library, as it will be possible to call it from a unit test framework.