Within the scope of a static cylindrically symmetric space-time we study the
behavior of a nonlinear spinor field that depends on time and radial
coordinates. It is found that the presence of nontrivial non-diagonal
components of the energy-momentum tensor (EMT) imposes some restriction on both
the metric functions and the spinor field. While for the time independent
spinor field there occur three way restrictions resembling the Bianchi type-I
Universe, in this case things become more complicated.