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A self-consistent system of nonlinear spinor and Bianchi type-V anisotropicgravitational fields are investigated. It is found that the presence ofnontrivial non-diagonal components of the energy-momentum tensor of the spinorfield imposes some severe restrictions to the system. As a result two differentsolutions are found. In one case the metric functions are similar to eachother, i.e., $a_1 \sim a_2 \sim a_3$ and the spinor mass and spinor fieldnonlinearity do not disappear from the system. In this case the spacetimeexpands with acceleration in case of a positive self-coupling constant$\lambda$. A negative $\lambda$ gives rise to a cyclic or periodical mode ofexpansion. In the second case the spinor mass and the spinor field nonlinearityvanish and the Universe expands linearly with time.

Nonlinear Spinor Fields in Bianchi type-V spacetime