Today, power generation is influenced by the electricity market and increased competition. Electricity buyers are free to choose their supplier. Instead of least cost method, which was used for planning and operational system management, power suppliers and generators are presently maximizing their profit. Today, the equilibrium is achieved in market settlement of generators' or suppliers offers and customer demand for electricity. Different methods and simulations exists that help in the consideration of market forces (water value, fuel costs, electricity price) and power generation costs. Short term maginal value became dominant in decision-making. The system is significantly complicated if we have constraints in the electricity transmission between the generator and the customer. Congestion means a situation in which an interconnection linking national transmission networks cannot accommodate all physical flows resulting from international trade requested by market participants. Congestion management became a dominant topic in the electricity market. The thesis deals with congestion management on cross-border transmission. With the opening of the electricity market and with merging or establishing regional electricity markets on the way through the internal electricity market in Europe, non-market based congestion management methods are being replaced with market-based methods. The thesis addresses the possible congestion management methods in view of of economic efficiency and promotion of competition, maximizing the amount of capacity available and the use made of it, transparency to network users on a non-discriminatory basis, secure network operation, largely revenue neutral mechanisms from the transmission system operator point of view.