Abstract: Research on the temporal relaxation of electrons in plasmas is of significance in plasma reactors, plasma light sources and gas lasers, etc. In order to study the temporal relaxation of electrons under the action of crossed electric and magnetic fields, electron transport and relaxation properties are calculated based on multi-term approximation of the Boltzmann equation. Firstly electron transport coefficients of Reid inelastic model are benchmarked. It is shown that when the reduced electric field E/n0 is equal to 12 Td lmax=7 is required in order to achieve four-digit accuracy of all transport coefficients. However, when the reduced magnetic field B/n0=500 Hx is switched on and the electric field is unaltered,lmax=2 is required in order to achieve four-digit accuracy of all transport coefficients. It can be inferred that the magnetic field can reduce the anisotropy of the electron velocity distribution.Our results are also compared with those obtained by Ness and White, et al. The results show the validity of multi-term approximation of the Boltzmann equation. Then the temporal relaxation of electrons in Reid inelastic model is studied. It is shown that relaxation of electron mean energy ε is monotonic while relaxation of bulk drift velocity WBz, bulk drift velocity WBx and diffusion coefficients n₀D_ii exhibit damped periodic decay. There is three distinct timescales: the electron gyration period γg, the momentum relaxation time γm and the energyrelaxation time γe. And the timescales satisfy γg＜γm＜γe. Bulk drift velocity WBx respond fastest to the action of the magnetic field, while bulk drift velocity WBz and diffusion coefficients n₀D_ii respond a little slower than the bulk drift velocity WBx and electron mean energy ε respond slowest. When the reduced magnetic field B/n0 is increased to 500 Hx, bulk drift velocity WBz have the same direction as the electric field E in the first oscillatory period, and there exist negative diffusion in the diffusion coefficient n₀D_xx.