Territorial organization of sub-national public power in contemporary states is unthinkable without decentralization and judicious distribution of responsibilities between levels of power achievement. These are the essential conditions of any process of territorial organization of public power. Decentralization of public power is a very current subject for Republic of Moldova. Power deconcentration, which was highlighted in the last two decades, is not enough for optimal functioning of public power and, also, for democratization of Moldovan society. It must take place concurrently with an extensive process of decentralization of public power. Decentralization is not an action of the moment, but one lasting over time and may be defined as a process associated with redistribution of functions and responsibilities between the public power authorities at different levels in order to achieve the most optimal results. Decentralization is important for strengthening of the local power as such, but equally it is particularly important to give up the practice of exercising the power on vertical line which is typical to post-Soviet bureaucracies which is still persisting in the public power system in Republic of Moldova.