The notions of admissible (almost) hypercomplex structure and almost contact hyper-Kahlerian structure are introduced. On a ¨ manifold M with an almost contact metric structure (M, ~ξ, η, ϕ, D) an interior symmetric connection ∇ is defined. In the case of a contact manifold of dimension bigger than or equal to five, it is proved that the curvature tensor of the connection ∇ is zero if and only if there exist adapted coordinate charts with respect to that the coefficients of the interior connection are zero. On the distribution D of an almost contact structure as on the total space of the vector bundle (D, π, M), an admissible almost hypercomplex structure (D, J, J ˜ 1, J2,~u, λ = η ◦ π∗, D) is defined. Under the condition that the admissible almost complex structure ϕ is integrable, it is proved that the constructed almost hypercomplex structure is integrable if and only if the distribution D is a distribution of zero curvature. In the case of a Sasakian structure (M, ~ξ, η, ϕ, g, D), the conditions that imply that the admissible hypercomplex structure (D, J, J ˜ 1, J2,~u, λ = η ◦ π∗, g, D˜ ) is an almost contact hyper-Kahlerian structure.