Let M be a connected C manifold of dimension n with a linear connection V . A method is being introduced here to study the action of the holonomy group and the restricted holonomy group of V on a recurrent tensor. The main result of this paper is that if the recurrence covector M of a recurrent tensor S on M is an exact form then the tensor S is invariant under the holonomy group of F and if H is a closed form then 5 is invariant under the restricted holonomy group of F . In the last section,

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... is result is applied to some particular cases including the case of a riemannian manifold with recurrent curvature.