A very efficient, strict nonstationary multi-term approach has been developed as a generalization of the conventional and the strict nonstationary two-term approximation used for solving the nonstationary electron Boltzmann equation. As a first application the temporal relaxation of electrons in a model plasma acted upon by a dc electric field has been investigated. The results are compared with corresponding ones obtained by the conventional and the strict nonstationary two-term approach as well as with very accurate Monte Carlo simulations. Perfect agreement between nonstationary eight-term Boltzmann and Monte Carlo calculations is found.