  Self-consistent system of nonlinear spinor field and Bianchi I (BI)
gravitational one with time dependent gravitational constant ($G$) and
cosmological constant ($\Lambda$) has been studied. The initial and the
asymptotic behaviors of the field functions and the metric one have been
thoroughly investigated. Given $\Lambda = \Lambda_0/\tau^2$, with $\tau =
\sqrt{-g}$, $G$ has been estimated as a function of $\tau$. The role of perfect
fluid at the initial state of expansion and asymptotical isotropization process
of the initailly anisotropic universe has been elucidated.
