Thanks a lot for trying to help me out! The main question you all ask is: "Do you have administrator rights?"
Well, I did a clean install of OS 10.4 some time ago. In the Help it says this: "When you set up Mac OS X, you create a user account that is also an administrator account." So therefore I have the admin rights.
I tried that out by creating other users and give them administrator priviliges. I just wanted to see that effect of "fast user switching". Well, that worked all right. After trying that out I deleted these accounts. So I am the only user on my computer.
In Preferences -> Accounts there is this box under the Adressbook card that should be ticked. That is the case.
Hope this clarifies my status as having an user account with Administrator privileges
Hope this gives more clarity.
Again thanks in advance!
I have been visiting Apple Discussions and found there that I could or should enable the root user. This could be done through the "NetInfo Manager utility" I had to set up a special root user password.
This worked fine and when I log in I can now choose between my "normal user" and the "root" Have to rush of to work now! )