This chapter attempts to provide a theoretical work on natural monopoly versus perfect markets through concentrating on the energy sector. In specific we discuss the natural monopolistic structure of Turkish natural gas and electricity markets by comparing those of various countries in Europe. In this vein, our chapter starts with the introduction of natural monopoly in both electricity and natural gas markets and the tools and regulations that targets on tackling this imperfection. Furthermore we present the historical phases of regulations to tackle natural monopoly in Turkish electricity and natural gas markets. Both price-demand and income-demand relationships are important guides for developing energy efficient programs for governments and hence income and price elasticities are channels for the relevant regulations. Armed with this in order to provide comparison, our chapter concludes with discussing the extent of the natural monopoly in each country through demonstration of income and price elasticities of demand for both electricity and natural gas.