This paper aims to analyse the stability of the global systemically important banks located in European countries between the 2008 and 2017, to find out whether the changing competitive environment affects the stability of these banks, and to determine variables with a significant impact on their stability. The stability is estimated by two proxies, Z-score and loan loss provisions, while the level of competition is estimated inversely by two indexes (market share and the Lerner index) expressing the market power of specified bank. We obtained the four main results. First: we provide evidence in line with the competition- -fragility paradigm when we use Z-score as a proxy of overall bank stability. Second: we provide evidence in line with the competition-stability paradigm when loan loss provisions measured loan stability. Third: our nonlinear investigation shows that around a specific turning point, the level of market power is likely to exacerbate the individual-risk-taking behaviour, and could be detrimental to the stability of the banking sector. Fourth: we showed that the increasing share of fixed assets on total assets, increasing bank liquidity, economic growth, and lagged stability measure had a positive impact on bank stability.