To give an up-date - after having 82 minutes phone support Apple found out this was caused by the program Beo Connect - a third party program from Bang and Olufsen.
After taking contact to Beo care I have received the following answer:
Thank you for contacting us. We are sorry to hear that you are experiencing problems with BeoConnect after upgrading to OS X Maverick.
We are aware of the problem and are working hard on a solution and will get back to you as soon as we can release an update for BeoConnect.
In the meantime, we can suggest the following work-around:
In 'Security and Privacy' for Mac - select Security, then Accessibility - allow for BeoConnect and iTunesDroper to control your computer.
However, this will require one login every time BeoConnect is used.
Kind regards,
Ina Bang Andersen (Ms) | Customer Service