Summary: The goal of this paper is to define intrinsically the Schouten-bracket. An important fact is that the introduced definition is available even in the infinite dimensional case. Our study is based on multi-derivations, introduced to this aim, which have remarkable properties. In the finite dimensional case, tensor fields are one to one with algebraic tensors. This is not the case in infinite dimensional context. For this, we consider “true” tensors. The Schouten-bracket is defined on this kind of tensor fields. Finally, as an application, we consider Jacobi algebras and Jacobi manifolds.