The achievement of competences is a good expression of the pertinence and efficacy of education programs in the different intervention fields. Social responsibility demands joint endeavors of interested agents, in procuring the sustainability. The creation of social awareness and compromise on the introduction of sustainability in social, economic, and environmental activities involves the consideration of sustainability concepts in all educational and occupational levels. Knowledge and practices in every discipline have meaning and value in particular contexts. A conceptualization of context is introduced in order to generalize the treatment of knowledge, curricular contents, and human, social, economic, and environmental responsibilities. Different strategies may be applied for the inclusion of sustainability concept in professional curricula and in the human competences, according to a model of context exigencies and a set of evolution categories. In our research, context concept is the central element in the definition and development of curricula, and in the achievement of competences. A contextualized development of Engineer's competences for sustainable development is the object of the present article. The proposed approach is illustrated in a Computer science engineering curriculum.