I realized that sometimes Eclipse forgets added libraries of a project. The problem is as follows. You can add a library to your Android project via:

Properties → Android → Library

I added a project to one of my projects that was set as Is Library. You can make a library out of an Android project, if you select the checkbox within the project properties:

Properties → Android → Library → Is Library

Let's call the library project proLib. The second project is named proInc that adds proLib into it's own list of libraries. You add the proLib library by clicking the right mouse button on the project folder and choose:

Properties → Android → Library

There you click Add from the right sidebar and select the proLib project out of the appearing list of libraries.
Click Ok and the library should appear in the tree of your proInc project under Library Projects.

Let's talk about my problem. I launched Eclipse and the system did not show the added library in the tree under Library Projects. I checked the settings at Properties → Android → Library and was confused by realizing that the requested library was correctly added to my project.

The solution. Just delete the added library from your project and add it again. That's it. The project will display the added library in the Library Projects entry and everything is fine.