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Hallo, welchen Listener kann ich denn verwenden, um abzufragen, ob die Maus über einem Button liegt und wann nicht mehr. (ohne Klicken!) Sozusagen, ab wann der JButton die farbige Umrandung bekommt und wann sie wieder verschwindet.

Use the ButtonListener for both classes. There ist still room for improvements, but this is a solution based on your code, that works. The ButtonListener now takes the calling JFrame as argument to close it when needed.