Despite decades of research on global leadership competencies, there is a continued unresolved debate among scholars around an integrative Global Leadership Competency model (GLC model), as none of the models proposed has been widely used in literature. Attempts to replicate and operationalize existing models are scarce, and scholars tend to recreate GLC models instead of building on existing ones. Instead of proposing yet another GLC model, this paper aims to identify factors that explain the unresolved debate around an integrative Global Leadership Competency model to be used in academic and managerial settings. To do so, we conducted a conceptual analysis based on an integrative literature review, where a sample of exemplar GLC models was surveyed and assessed. This analysis resulted in the identification of three conceptual incongruences, namely 1) varying assumptions regarding the meaning of competency; 2) divergent model structuring; and 3) varying delimitation, resulting in varied sets of competencies. These incongruences relate to diverse assumptions, perspectives and interpretations that are inherent to the development of GLC models, but often not explicitly acknowledged and addressed by studies. We argue that these incongruences hinder scholars’ and practitioners’ capacity to evaluate, compare and contrast different models, and may therefore explain the unresolved debate around an integrative GLC model. While grounded in global leadership theory, this article also contributes to cross-cultural leadership and management scholarship by providing a critical discussion about the competencies required by leaders to operate effectively in a global environment, where they are required to manage across different cultures and socio-economic contexts.