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Let $G$ be the identity component of the isometry group for an arbitrarycurved two-point homogeneous space $M$. We consider algebras of $G$-invariantdifferential operators on bundles of unit spheres over $M$. The generators ofthis algebra and the corresponding relations for them are found. The connectionof these generators with two-body problem on two-point homogeneous spaces isdiscussed.Comment: LaTeX, 38 pages, 1 figure, octonionic case was included in the 3-rd  version, some errors were corrected in the 4-th on

Algebras of invariant differential operators on unit sphere bundles over two-point homogeneous Riemannian spaces