At the turn of the XX – XXI centuries, there is a certain "fatigue" in the humanities from the term "postmodern" / "postmodernism", various works appear summarizing and offering alternative concepts to describe modernity. The article attempts to analyze the arguments in favor of preserving or replacing the concept of "postmodernism", advanced by theorists, many of whom participated in the initial discussions about "postmodernism". In order to identify the essential markers of this concept, formulated initially by Western researchers rather amorphously and vaguely, the authors of this study analyzed individual texts of both pioneer theorists, which undoubtedly include Ihab Hassan, Fredrik Jamieson, Brian McHale, Terry Eagleton, Linda Hutcheon, and scientists who joined the debate later: Alan Kirby and Stuart Jeffries. The conceptual basis of the article is the theory of F. Jamieson, who defines "postmodernism" as the cultural dominant of capitalism at its "late" stage. The comparative method is used in the course of the study. The following grounds of criticism are revealed: the initial failure of the term, its semantic uncertainty (I.Hassan); institutionalization, lack of a theory of political agency (L. Hutchenon, T. Eagleton), overestimation of universality (B. McHale, T. Eagleton); obsolescence and inconsistency with modern realities (A. Kirby). On the other hand, F. Jamieson retains his previous argumentation, abandoning the very term "postmodern" / "postmodernism" in favor of "globalization", and makes some corrective changes. S. Jeffries believes that new technologies have accelerated the spread of postmodernism and contributed to its revival. Such ongoing discussions suggest that the concept of "postmodern" / "postmodernism" retains a certain heuristic potential, and, according to the authors, radical socio-economic and environmental changes pose a real threat to it.