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Introduction: Energy return on energy invested (EROEI) of fossil fuels has been declining sharply, while modern renewable energy sources generally have even lower EROEI than fossil fuels. It has been repeatedly proven that economic growth expressed in the form of growth of real Gross Domestic Product (GDP) is closely related to intensified energy consumption and escalated usage of natural resources in general. This problem remains scarcely explored in pure economic modelling. Objectives: This study presents a novel model titled Energy Extended Neoclassical Growth Model (EENGM), which focuses on the consequences of declining quantity and quality of extractable fossil fuels and lower quality of the succeeding renewable energy technology for economic growth. Method: The Neoclassical growth model is translated into a system dynamics format and is extended by important feedback mechanisms, which are identified as important from the literature and mostly missing from the analyzed system dynamics models with a similar scope. Two scenarios assess the EENGM performance: business as usual (BAU) and the sustainability strategy (SUS). Results: Sensitivity analysis is performed for the Energy Return on Energy Invested (EROEI) parameter and results in the investment share in GDP varying between 27 and 40%, while the energy sector investment largely displaces investment in other economic sectors. The EENGM is associated with new behavior whereby the underperforming energy sector limits GDP growth and seizes most of the available investment. The adoption of the SUS strategy causes 28% lower cumulative fossil fuel aggregate consumption which still corresponds to higher than 1.5 degrees C global warming compared to the preindustrial levels. Conclusion: The share of consumption in the GDP of an economy undergoing energy transition can approach levels previously seen only in totally war-oriented economies. Even omitting other negative environmental feedback, the feasibility of the successful energy transition of the system in its contemporary form, with the currently available renewable energy technology, seems to be highly uncertain.