We present a general study of the dynamical properties of Anisotropic Bianchi Universes in the context of Einstein General Relativity. Integrability results using Kovalevskaya exponents are reported and connected to general knowledge about Bianchi dynamics. Finally, dynamics toward singularity in Bianchi type VIII and IX universes are showed to be equivalent in some precise sence. HOMOGENEOUS UNIVERSE AND BIANCHI MODELS Considering the usual synchronous frame of General Relativity 1 ds 2 = g µν dx µ dx ν = ˜ g i j dx i dx j − dt 2. A Universe is said homogeneous when there exists an isometry group wich preserves the infinitesimal spacial lenght dl 2 = ˜ g i j dx i dx j A characterization of the isometry group is possible writing structure constants C