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Emergence of energy markets in all the countries of the European Union is now a reality. In Greece, liberalization of the electricity market entered into effect the 19th February 2001. This paper deals with the Hellenic energy market structure and operation, as handled by the Hellenic Transmission System Operator (HTSO), who acts as a system operator and market operator. In compliance with the Hellenic market rules, the optimization-based framework for solving the market-based realtime dispatch problem is presented. Hydros vs. thermal dispatch specificities are described and numerical examples are included to illustrate them.