In this paper we study a new structure, called a spinnable structure, on a differentiable manifold. Roughly speaking, a differentiable manifold is spinnable if it can spin around a codimension 2 submanifold, called the axis, as if the top spins.The main result is the following: let $M$ be a compact $(n-1)$-connected $(2n+1)$-dimensional differentiable manifold $(n\ge 3)$, then $M$ admits a spinnable structure with axis $S^{2n+1}$. Making use of the codimension-one foliation on $S^{2n+1}$, this yields that $M$ admits a codimension-foliation.

On donne une construction de formes de contact sur toute variété décomposable en somme connexe de variétés de contact en toute dimension.