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A novel model for the clearing of European day-ahead electricity markets, with all associated types of orders, namely simple hourly orders, block orders, complex orders and PUN (“Prezzo Unico Nazionale”) orders is presented in this paper. An iterative algorithm is employed for the market clearing, bearing an inner iteration process for the handling of Paradoxically Accepted block and MIC orders, and an outer iteration process for the handling of PUN orders. During the iterative process a Master Problem and a PUN subproblem are sequentially solved and coordinated, for the efficient handling of all order clearing conditions and market and/or system constraints. The clearing conditions of each order type are explicitly incorporated in the PUN subproblem, formulating a Mixed Complementarity Problem bearing both primal and dual decision variables. The PUN subproblem concerns the sequential clearing of 24 hourly subproblems, employing a special technique for handling the possible inefficiencies due to the myopic nature of the hourly subproblem solutions, leading to enhanced behavior in terms of social surplus with respect to the state-of-the-art day-ahead market clearing solver. The model and the algorithmic process are evaluated in a west-European test case, demonstrating minimal computational requirements and proving its excellent escalation capabilities. [ABSTRACT FROM AUTHOR]