The aim of the present paper, we have studied almost hyperbolic Hermite manifolds and also obtain a few interesting results. Almost contact hyperbolic (f,g,h,x) structures have been defined by M.D. Upadhyay and K.K. Dube⁷ and others. Vanzara⁸ studied almost r-contact structures. The paper is organized as fallows. Section1, contains a brief introduction to hyperbolic Hermite and Nijenhuis tensor, while in section 2 some necessary details about some results of manifolds are presented. In section 3, we define affine connections of D in mⁿ and a vector valued bilinear function of torsion tensor.