Hi Tilo,
Are you definitely logged in as a Super Admin on the front-end too? Make sure you are visiting the site with either both www in each of the Control Panel URL and the front-end URL or both without the www. If you go to one of them with a www and the other without then these are seen as different domains due to the cookies on the site. If you fill in the Cookie preferences though then you can stop this from happening again.
You might want to use something like this in your template too to see if you really are logged in as a Super Admin :
{if member_group == "1"}
Logged in as a Super Admin
{/if}
{if logged_in}
You are currently logged in to the member group with the ID of {member_group}
{/if}
{if logged_out}
You are currently logged out of the system
{/if}
The code above should give you all the information you need to see if you are indeed logged in under the correct member group.
Hope that helps a bit.
Best wishes,
Mark