In some previous papers [ibid. 42, 283-298 (1985; Zbl 0593.53022)] the authors constructed in an original way a theory of hypersurfaces \(M_{n- 1}\) in a Finsler space \(M_ n\). In this theory the first author gave some special connections, named TMD-connections. In the present paper the connections ITMD are considered, induced on \(M_{n-1}\) by a TMD- connection in \(M_ n\). The intrinsic connections of \(M_{n-1}\), totally geodesic hypersurfaces and some interesting properties of them are studied.