The invention relates to the problem of the driving of the LCD electrooptic-switching element (1) with alternating, square-wave electric signals, the amplitude of witch can vary between different voltage levels in correspondence with the actual functioning state of the LCD electrooptic-switching element. The polarity changes of the electric driving signals is controlled by the integrator (9), integrating the difference of the electric potentials on the driving electrodes (2, 3) of the LCD electrooptic-switching element, in such a way that the value of time integral of the driving electric field is always kept within a selected interval. Besides this the time dependence of the electric driving signals can be optionally modified so that with every change of the polarity of the electric driving signals, the potentials on both driving electrodes get the same value for a time, which is significantly shorter than the switching time of the LCD electrooptic switching element.