Internet connection crashes while wifi / lan stay connected

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http://askubuntu.com – I am connected to a router by wifi or lan. But every few moments (sometimes seconds, sometimes half an hour) my connection to the internet breaks down. So in one moment I can surf with my firefox and have ping times of 20 ms (wifi) to the google server. And in the next moment I can't open any pages in any browser and the ping shows no new messages first and then "Destination Host Unreachable". This is especially odd as another computer or my smart phone stays connected at the same time to the same network and seems to notice nothing. So I have a problem independend of wifi or lan drivers b (HowTos)