Prince Harry -- Kicking Alexander Skarsgard's Ass in South Pole Race

Prince Harry and the Brits are handing down a royal ass whupping to Team USA -- led by 'True Blood' star Alexander Skarsgard -- during their epic race at the South Pole, and TMZ has the footage.

In case you missed it -- Harry, Alexander, and Dominic West from "The Wire" are each leading teams on a 208-mile journey across the South Pole for the Walk with the Wounded race.

TMZ had the first pics of the teams training -- and one week into the competition Team UK is in first ... followed by Team Commonwealth (led by Dominic) ...while Skarsgard's U.S. crew is bringing up the rear.

Check out the video ... and be glad you're not down there.