stalemate ened when Germany fired The Ludendorff Offensive, a series of attacks. It lead to the furthest advance from 1914 to March 1918. But then Britain and France started to fight back and a couple of months later the Germans surrendered!
Would you mind reposting your question with a little more information? There was a stalemate in most of World War I, but World War II happened in so many places, that I do not know of the occurence...
The war petered out because the United States completely failed in it's objectives, and the British had no intention of attempting to undo American independence, but it was not a war without winners...