The Challenger is on the left, the Alpha is on the right. There isn't much jockeying for position. The whole thing lasted about 10 minutes. The fight starts when the challenger starts braying at the Alpha. .

The alpha is only too willing to defend his claim.

They belly up to one another so they can try to judge each other's size (and presumably experience.) This particular challenger looks like he's been making quite a few challenges. You can see from his chest shield that he's been in several fights.
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Then they start the actually fighting. This part doesn't last long. They swing their heads and trunks at one another. The one being hit makes no attempt to evade. After the first few hits, they start taking bites as they hit. This is why they look bloody afterward.

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As is apparently usual, the old alpha wins this fight, and the challenger slinks off. The one we saw didn't move fast enough or far enough for the old guy, so the old guy chased him a little to make sure he understood the message. Afterward, the alpha went back to sleep.
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