It seems that i found a solution for my problem:
Using socket number 3 all pings are successful.
I expanded the ping-example with the WebServer example (from the Ethernet library) and with socket #0 and 1 i had no success.
Then i tried socket number 3 in my own application and since then everything is fine.
Thanks to Blake for this routine. I tried to examine the source but it is really tricky and goes very deep so i didn't try to make any changes.
Klaus