Any reflections on an eventual transition towards a degrowth society have to take into account the current crisis in the dominant system and question whether the latter will be able to grow again or not. In order for the latter to happen, the role played by technological innovation is crucial. This paper starts by reconsidering Georgescu-Roegen’s definition of Promethean Techniques and Tainter’s principle of Declining Marginal Returns, with the aim of providing – within the common framework of the theory of complex systems - a sound theoretical basis for the analysis of the rise and fall of complex societies. The main purpose is to verify whether, after the last Promethean revolution, a “Great Wave” emerged or not. The second part of the paper presents an initial investigation into this hypothesis, using Total Factor Productivity growth as an indicator of (marginal) returns on innovation (1750–2015). Despite the limitations implicit in the use of this indicator, data show three cycles of innovation, corresponding to the first, second and third industrial revolutions, but of different magnitude and duration. In particular, the whole cycle that began with the first industrial revolution in England around 1750, reached a peak in the U.S. in the nineteen-thirties and later declined, following a trend that basically confirms the Great Wave hypothesis. Even recent innovations resulting from the ICT revolution, however considerable, do not seem capable of counteracting this long-term trend. Data on returns on innovation seem, therefore, to be coherent with evidence provided by research in other fields (energy, mineral resources, agriculture, health, education and scientific research), showing that advanced capitalist societies have entered a phase of declining marginal returns - or involuntary degrowth - with possible major effects on the system’s capacity to maintain its present institutional framework.