Entering the European Union faces the actual challenge to implement the European dimension into the educational process. The term "European dimension" itself is contradictory because it can be interpreted differently: an element of the educational change in Europe; the factor, the incentive and the helpful condition for the change; contents of education which is realised through curriculum; interdisciplinary relations; the dynamic reality. For the school participating in the European partnership the most actual goals of introducing the European dimension are: to reinforce the European identity and achieve that people were obvious about the value of the European civilization and that the present development of Europe is based upon democracy, social justice and protection of human rights; to strengthen their knowledge about the European Community and its member states in historic, cultural, economic and social aspects; to comprehend the significance of partnership among the EU member states and other countries of Europe and the world. (The European dimension in the curriculum of the primary school ..., 2002, p. 3). The European Commission report "Towards a Europe of Knowledge" (1997) points out three fundamental directions for developing the European dimension in education: knowledge, citizenship, competence. Here occur broad possibilities to implement the European dimension into the curriculum of schools taking part in the European school projects and enhance the potential of the development of children's competency. The goals of the international project can become the integral part of the local and national curriculum and can be realized throughout the lessons, in after curricula activities, while realizing integrated learning. The curriculum here is understood not only as the program or teaching contents but as different pedagogical and organizational activities in and beyond the school. The paper stresses the opportunities and insufficiencies of realization of The Cubic Curriculum in European School Projects. It consists of five parts. The first part conveys description of the Curriculum, the contemporary viewpoint on it and the challenging aspects of its implementation. The paper analyses possible alternatives of its interpretation: the educational program with goals, contents, forms and methods of realization; an individual educational program; actions the active participants of which can become all the school community members. The second part presents the unique viewpoint of professor in Education E.C.Wragg at Exeter University who sees the curriculum as a cube having three principal dimensions of subject matter, cross-curricular themes and issues that influence children's general development and different methods of teaching and learning which can be employed. This viewpoint of the The Cubic Curriculum makes the methodological foundation of the paper. The third part substantiates that The Cubic Curriculum proposes larger possibilities for incorporation of the European dimension into the school curriculum in European school projects. It displays the facts illustrating that the European school partnership influences not only the change and development of the curriculum but the school as institution, the usage of ICT in distant cooperation, the raise of the ICT competence of the whole school, the development of the pedagogical, methodological and didactic components of a school, enriches culture of the institution. The fourth part analyses the case study of Comenius School project "Children's Games" and embraces the incorporation of the European dimension into The Cubic Curriculum. In the fifth part, the data of opportunities and insufficiencies that can occur during the realization of The Cubic curriculum in European school projects are also revealed.