Most of Business Excellence – Total Quality models provide a static view and processing of Total Quality issues. This paper proposes a system of Business Excellence taking into consideration: current European practices of Total Quality and competitiveness, a modular, open architecture like this in computer networking, calculation of the performance and effectiveness of the approaches, rather than enablers and results in separate and a system Dynamics to support interdependence and correlation of system variables. The paper, also, reviews some major European National Quality Awards to identify routes of tendencies and proposes in general terms the structure of the business excellence system. The research is based on information gathered by bibliography, by own findings, as well as, by issues provided from the first implementation of the Hellenic National Quality Award by the Ministry of Development. Research findings showed that EU countries do not have a common framework to address business excellence, however the “European Quality Award” (EQA) based on the “EFQM Excellence Model” is the most widespread in the previous decade. There is a tendency towards own developments on national quality awards in the current decade. There is also a clear indication of Quality Awards ‘nature’ across EU: there are the ‘national ones’ which are supported by their governments in the sense of financial support to organisations and the ‘private ones’ which are supported by associations, chambers, private organisations and non profit organisations. In addition, a Business Excellence System is proposed to verify this European tendency of own developments providing a modular and open architecture of Total Quality practices or developments.