Since the Blu-ray Disc and HD-DVD formats are incompatible, due to differences in actual physical disc structure, you cannot play a Blu-ray Disc in an HD-DVD format player, nor can you play an HD-DVD in a Blu-ray Disc format player.
However, if you own one of the few Blu-ray Disc/HD-DVD players that were made by LG (LG BH100/BH200) or Samsung (BD-UP5000), these players can play both Blu-ray and HD-DVD discs.
As a note of trivia, Warner Bros actually developed a disc that was Blu-ray on one side and HD-DVD on the other, with the idea of releasing movies in both formats on a single disc, but the effort was not adopted by either the Blu-ray or HD-DVD backers, so was never realized as a product.
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