The electron transport equation for conductors under electric fields which vary both in space and time is developed quantum-mechanically. The case where electrons are scattered elastically by static impurity centers and the case where inelastically by phonons are treated separately. The equation derived here has a new extra term, which represents the coupled effects of electron collisions with impurities or phonons and electron motions by the external oscillating fields. This term plays an important role in high frequency regions, though vanishes in the static limit. The conductivities in the static limit and in the high frequency limit are given from special solutions of this equation.