We present first-principle evaluations of the electron-phonon coupling strength parameter and associated characteristics of relaxation for the excited electrons in the conduction band of zinc oxide. The evaluations are based on the pseudopotential plane-wave approach to the electronic band structure, the density-functional perturbation theory for the calculations of phonons and electron-phonon interactions, and on the "Fermi golden rule" for evaluations of the electron relaxation time and the energy-loss time. The calculations demonstrate existence of two types of electron dynamics, the picosecond one for electrons near the bottom of the conduction band and the femtosecond for the higher energies. Sensibly good agreement with experimental data confirms the validity of the calculations.