Given that sustainability is about a good human life for all human beings living today and in the future against the backdrop of existing scarcity and fragility of environmental resources, one of the main critical and vividly discussed topics within the scholarly sustainability community concerns how to meaningfully conceptualize intra- and intergenerational justice. More recently, a number of authors have started to invest the Capability Approach (CA) as a normative basis to conceptualize sustainability.  However, at least two critical fields build barriers for such a conceptual endeavor. First, the CA is understood as a group of theoretical components rather than a clear and unified theory. Accordingly, it is not clear what exactly is invested when investing the CA. Second, as the CA has thus far neglected environmental issues, the question remains whether or not it can be used for sustainability without expanding its conceptual basis. Against this backdrop, this PhD-project strives for contributing to a better clarification of the conceptual basis that the CA could provide for working out a conception of inter- and intragenerational justice as core-elements of sustainability by answering the research question: Does the CA have to be theoretically expanded to serve as a normative foundation for SD? To achieve this end, there are five steps taken: (i) outlining the sketched problem in question to demonstrate the rationale of the research question; (ii) reviewing the current state of and options within the CA; (iii) identifying possible discrepancies between the CA and requirements for a sustainability conception; (iv) discussing possible theoretical extensions of the CA and finally; (v) interpreting the identified extensions as either inherent to the CA or real extensions. The result will lay the groundwork for the development of a capability based sustainability conception.