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In this paper we develop a model for the capabilities required by principals for effective Science, Technology, Engineering and Mathematics (STEM) leadership. The model underpinned a large national cross-sectional research and development project across Australian states in both primary and secondary schools. This model is developed via synthesis of research literature across leadership and STEM education. The model consists of five dimensions of principals' STEM capability: (1) STEM discipline-specific and integrated knowledge and practices; (2) contexts; (3) dispositions; (4) tools; and (5) critical orientation. These dimensions represent distinct, but interrelated, capacities required by principals to establish and maintain positive STEM learning cultures within schools. Elaborations have been provided, in the form of capabilities, for each of these dimensions. The model has the potential for shaping principals' STEM leadership development trajectories and structuring targeted professional learning programmes for principals, teachers and other members of the school community. [ABSTRACT FROM AUTHOR]