The mechanism of anode-initiated breakdown in liquid organic dielectrics with long molecular chains is proposed on the basis of the experimental data on high velocities of the breakdown channel propagation in organosilicon and organofluorine liquids (~10^{7} cm/s), which is comparable to that obtained earlier in crystals in the same conditions. The high velocities of the anode-initiated breakdown channel are satisfactory explained within the model of the cascade Auger transitions, developed for the crystalline materials. According to this model, velocity of the breakdown channel propagation is proportional to the electrical field strength. The time delay in breakdown channel formation relative to the voltage pulse front does not exceed ~5·10^{-10} s within the margin of error.