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We obtain a complete classification of hypercomplex manifolds, on which acompact group of automorphisms acts transitively.  The description of the spaces as well as the proofs of our results use onlythe structure theory of reductive groups, in particular the notion of "stem" ofa reduced root system, introduced in the first paper of this series.

Homogeneous Hypercomplex Structures II - Coset Spaces of compact Lie Groups