The Hellhound (also known as the Beast Of Darkness) is a creature which sometimes appears to Guts, taunting him, questioning the morality of his quest for revenge, and urging him to commit ever-greater atrocities, most notably attempting to convince him to rape Casca. While it at first appears to be a demon or evil spirit of some kind, it also appears to Guts inside Godo's cave which evil spirits cannot enter. This would seem to imply that it is either a hallucination or otherwise a part of Guts' mind.
The Hellhound might be the embodiment of Guts' own rage and hatred at the God Hand, the Apostles and especially Griffith after the Eclipse. Among other things, it wants Guts to kill Casca so that he can get back to seeking revenge.
The fact that in the past (volume 5, chapter 3: Wind of Swords) Casca shouted in anger to Guts that he is just a "mad dog" it is probably the reason why his inner beast is represented as the Hellhound.
When Guts uses the Berserker armor, the helmet appears very similar to the Hellhound's head. The Hellhound appears to be strengthened by repeated use of the armor, but is held in check by Guts' affection and loyalty for his companions. These two forces are constantly at odds: in his latest appearance, the Hellhound seemed larger and stronger than ever, but was bound by thick chains. However the Hellhound has vowed should the time come when Guts was too weak to subdue him, the Hellhound would break free and take over Guts and kill all those Guts held dear.
Vova
