Several personality models are known for being replicable across cultures, such as the Five‐Factor Model (FFM) or Eysenck's Psychoticism–Extraversion–Neuroticism (PEN) model, and are for this reason considered universal. The aim of the current study was to evaluate the cross‐cultural replicability of the recently revised Alternative FFM (AFFM). A total of 15 048 participants from 23 cultures completed the Zuckerman–Kuhlman–Aluja Personality Questionnaire (ZKA‐PQ) aimed at assessing personality according to this revised AFFM. Internal consistencies, gender differences and correlations with age were similar across cultures for all five factors and facet scales. The AFFM structure was very similar across samples and can be considered as highly replicable with total congruence coefficients ranging from .94 to .99. Measurement invariance across cultures was assessed using multi‐group confirmatory factor analyses, and each higher‐order personality factor did reach configural and metric invariance. Scalar invariance was never reached, which implies that culture‐specific norms should be considered. The underlying structure of the ZKA‐PQ replicates well across cultures, suggesting that this questionnaire can be used in a large diversity of cultures and that the AFFM might be as universal as the FFM or the PEN model. This suggests that more research is needed to identify and define an integrative framework underlying these personality models. Copyright © 2016 European Association of Personality Psychology