As a result of globalization, kindergarten curriculum frameworks in Asia have been strongly influenced by Western theories, pedagogies, and values. In this article, we argue that Singapore's Nurturing Early Learners and Hong Kong's Kindergarten Education Curriculum Guide present key notions that are inconsistent with cultural values that are deeply rooted in these two societies. To overcome the challenges these inconsistencies trigger for teachers, principals, teacher educators, and parents, we advocate for the design of 'glocal' (global/local, explicitly hybrid) curriculum frameworks, based on principles that are culturally appropriate and socially situated. Drawing on recent research studies, we analyze current curriculum/practice gaps in relation to the notions of Child-Centeredness, Quality Interactions, Creativity and Self-Expression, and Play. In seeking the global/local balance that is needed in Singapore and Hong Kong, four alternative glocal notions are proposed: Child-Appropriateness, Pedagogical Quality, Arts Engagement, and Child-Led Activities. We conclude there is an urgent need for generating a solid corpus of local research in both jurisdictions, which should guide subsequent curriculum reforms and teacher preparation models. Our final aim is to contribute to early childhood education policy discussions in Asia, against the background of internationalization. Copyright © 2020 The Author(s).