  Qualitative approach to homogeneous anisotropic Bianchi class A models in
terms of dynamical systems reveals a hierarchy of invariant manifolds. By
calculating the Kovalevski Exponents according to Adler - van Moerbecke method
we discuss how algebraic integrability property is distributed in this class of
models. In particular we find that algebraic nonintegrability of vacuum Bianchi
VII_0 model is inherited by more general Bianchi VIII and Bianchi IX vacuum
types. Matter terms (cosmological constant, dust and radiation) in the Einstein
equations typically generate irrational or complex Kovalevski exponents in
class A homogeneous models thus introducing an element of nonintegrability even
though the respective vacuum models are integrable.
