Thanks a lot, there are some very useful hints here.

I finally can manage to do the "purring" sound, though at the moment it sounds more like the firing of a tractor engine than the purring of a cat... I hope practice will help. With the "Eddie" hint I have more problems, but I won't give up so fast.

If anyone is interested: German "r" can either be produced in the throat or in the front of the mouth ... depends on the region the people comes from. So in the south it's more often produced in the front and in the north it's mainly the throaty "r". Both are accepted but the throaty r is more common.
For the "throaty-r": say the German "ch", soften the airstream and try to get the uvula-part or your mouth to vibrate. Practice that a bit, and then try to make an "r" with your vocal cords in addition. So the "r" itself is mainly produced by the vocal cords, but get's it's throaty quality by the vibration of the uvula-mouth-part. Hope that helps a bit.

And yes I agree that having the opportunity to watch a native when he is speakin is very helpful. Though personally I wouldn't like it very much when people were staring into my mouth - reminds me too much of the dentist.

Vielen dank!

My German teacher keeps saying that the "front r" is okay but I only hear the throaty one in her audio tapes so that made me wonder. I think I'll stick to trying the throat r until I get a soar throat and then switch to the easier one.

By the way. The "front r" kinda sounds to me to be pretty much the same "purring" that I wrote about, or is it somehow different? :/