In Finsler geometry, most of the special Finsler spaces are characterized by the special forms satisfied by the torsions and curvatures tensors associated with Cartan connection. Consequently, special spaces in Finsler geometry are much more numerous than those of Riemannian geometry. Special Finsler spaces are investigated by many authors. One of the most famous of them is H. Akbar-Zadeh. The aim of the present paper is to prove two intrinsic generalizations of the important Akbar-Zadeh's theorem on Finsler spaces of constant curvature. Some consequences of these generalizations, concerning S_3-like and〖 S〗_4-like spaces, are drown