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

On solutions of the Pauli equation in non-static de Sitter metrics