The idea of f -structure manifold on a differentiable manifold was initiated and developed by Yano [1], Ishihara and Yano [2], Goldberg [3] and among others. The horizontal and complete lifts from a differentiable manifold M n of class C ∞ to its cotangent bundles have been studied by Yano and Patterson [4,5]. Yano and Ishihara [6] have studied lifts of an f -structure in the tangent and cotangent bundles. The purpose of this paper is to obtain integrability conditions of a structure satisfying F K − ( − ) K + 1 F = 0 and F W − ( − ) W + 1 F ≠ 0 for 1 < W < K , in the tangent bundle.