Introduction. The widespread adoption of generative language models raises questions regarding user competence. Existing component models of AI literacy identify a range of necessary competencies but do not organise them hierarchically. Level-based digital competence frameworks fail to account for the specific characteristics of generative AI, while Bloom’s taxonomy does not encompass the metacognitive, pragmatic, and ethico-social dimensions of human-AI interaction. Aim. The present study aims to develop and theoretically substantiate a hierarchical model of meta-digital competence specific to interactions with generative language models. Methodology and research methods. The study employs theoretical modelling. The hierarchical model was developed through a critical analysis of component AI literacy models, level-based digital competence frameworks, Bloom’s taxonomy, and theories of distributed cognition, metacognition, situated learning, and responsible AI principles. Results. A five-level MDC model was developed, comprising the operational, cognitive, reflexive, pragmatic, and ethico-social levels. Behavioural indicators and achievement criteria were defined for each level. The ethico-social level is positioned at the top of the hierarchy, as ethical responsibility integrates all preceding levels. Scientific novelty. The scientific novelty lies in the development of a hierarchical model specific to generative AI interaction; demonstrating the insufficiency of Bloom’s taxonomy for a comprehensive description of this competence; identifying the pragmatic level, which has no equivalent in existing component AI literacy models; and theoretically justifying the placement of the ethico-social level at the apex of the hierarchy. Practical significance. The practical significance resides in the potential application of the model for designing educational programmes, developing diagnostic tools, and creating assessment procedures aimed at the sequential development of meta-digital competence.