The processes occurring on the electrodes and in the liquid phase during the arc discharge in the liquid phase (ADLP) have been considered in the present work and we explain the mechanism of carbon nanostructures (CNS) formation proposing the model based on the analysis of existing regularities in behaviour of charged particles under extreme temperature and pressure gradients. The CNS synthesis by ADLP method has been performed in dielectric liquids: hydrocarbons, liquid gases (N₂, Ar, He, etc.), deionized water and others. Suspension containing clusters of synthesized nanostructures has been formed by the synthesis. The efficiency of this method is sharply increased by using arc discharge in the liquid phase where powder reagent layer is used as anode. To increase the frequency of electrodes clamping and moving apart, an electromagnetic vibrator has been used in this method and it brings and takes away the cathode from the powder reagent at a specified frequency. For ADLP, nanostructures form simultaneously at several points on the conducting particle surface as a result of microscopic acts of arc discharge. These nanostructures are generated from the liquid phase and anode vapors and represent the product exhibiting rather interesting physical and chemical properties. Based on the analysis of the observations performed in the course of carbon nanostructures synthesis, the model of nanostructures formation by arc discharge in the liquid phase has been proposed in this paper. Presence and absence of deposit on the cathode have been explained.