This is a study of transdisciplinary teaching of education for sustainable development (ESD) with a global dimension at an upper secondary school in Sweden. The paper examines the argument that in these contexts, content and teaching forms are not established in advance, making it possible for students to develop critical knowledge capability, and go beyond simply holding a competence for acting in a defined and foreseeable situation that can be practiced in advance. Knowledge capabilities allow students to take adequate decisions in the future, as new situations occur and demand action-taking. 27 semi-structured interviews were conducted with 9 teachers and analysed using phenomenographic and contextual analysis. Two main approaches to transdisciplinary teaching were identified: one where they contributed but struggled with transdisciplinarity, and the other where teachers displayed ownership and were able to reconceptualise the project as a whole. Overall, teachers worked in the project with deep-level processing for learning ESD in an integrated manner in a transdisciplinary framework. However, they experienced tensions between their resources and capabilities, and the challenges in devising learning activities and support structures for students that involve various dimensions. Despite their aspirations to achieve ESD learning goals expressed in the national curriculum, teacher teams frequently experience that they do not have full capability to cover a complex knowledge field. The paper concludes by arguing that by enhancing the ability to deal with global processes, involving critical thinking, skills and values, ESD inevitably attempts to foster students becoming responsible citizens. This is facilitated by approaches that - from the outset, integrate global and transdisciplinary dimensions, and thereby address the challenge of teaching about complexities with considerations of local situations, and diverse values or cultures. Importantly, working with the global dimension allows students to better understand conflicts of interest underlying different suggestions for dealing with sustainability issues.   The paper addresses the main conference theme and in particular the subtheme: New epistemologies and new forms of knowledge within the North-South dialogue.