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The torsions of a general connection $\Gamma$ on the $r$th-order tangent bundle of a manifold $M$ are defined as the Fr\"olicher-Nijenhuis bracket of $\Gamma$ with the natural affinors. The author deduces the basic properties of these torsions. Then he compares them with the classical torsion of a principal connection on the $r$th-order frame bundle of $M$.
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