I have this page: http://www.nemkontoret.dk/ny/ where I have been trying to highlight the active menu item.
If i go to a 1st level menu item where there is 2nd level menu items, it will highlight all the 2nd level menu items.

How can I stop that?

Thank you!!

First of all "active" in css refers to the item when it is clicked on (mouse button down) and does not refer to it's status as current. You need to use a tool like Firebug on Firefox to determine the CSS selector for the current state and write some CSS to set the background etc to whatever color you wish.

I have tried to do so, but can't figure out why 2nd level menues are highlighted when I click on a 1 st level menu item.

The CSS i have found is this: li.current-menu-item a

It works fine if there is no 2nd level menu item

Now you have to write some code for the sub-menus if you don't want them to be highlighted.

How to do that??

It is working like I want when I am standing on a submenu item.
I just don't want 2nd level to be highlighted when standing on a 1st level item.

Everything else is working perfect.

Without knowing more about what you have done this is not a simple "here is the code". I would need to install the menu plugin you are using and spend time seeing how to tweak the colors. Then I would need to know what you have already done for styling on your site. Also perhaps the menu plugin creator has some thoughts on styling.