I don't recall them ever waging war. As a matter of fact, they never meet in the entire story of Beowulf. If its a question about the book “Grendel” then yes they do meet but still don't wage war against each other. read more
In the Beowulf poem Grendel and the dragon do NOT wage war. Beowulf kills Grendel in the first half of the poem, that takes place in the kingdom of Hrothgar. Then, fifty years later in the kingdom of the Geats, of which he is king, Beowulf kills the dragon. read more