  A particle with spin 1/2 is investigated both in expanding and oscillating
cosmological de Sitter models. It is shown that these space-time geometries
admit existence of the non-relativistic limit in the covariant Dirac equation.
Procedure for transition to the Pauli approximation is conducted in the
equations in the variables $(t, r)$, obtained after separating the angular
dependence of $(\theta, \phi)$ from the wave function. The non-relativistic
systems of equations in the variables $(t, r)$ is solved exactly in both
models. The constructed wave functions do not represent stationary states with
fixed energy, however the corresponding probability density does not depend on
the time.
