In response to the 2007-2008 global financial crisis, the G20 mandated the Basel Committee to put in place prudential regulations capable of ensuring financial stability: the Basel III agreements. This paper tackles this issue by investigating the impact of capital and liquidity ratios on financial stability for a sample of 1600 banks from 23 countries over the 2005-2016 period. We pay particular attention to the nonlinear character of this potential effect through the estimation of a polynomial model with interaction terms and a panel smooth transition regression. Distinguishing between different types of banks depending on their level of systemicity, we find evidence of a nonlinear effect of prudential ratios on financial stability: a low level of capital improves financial stability, but its effect tends to diminish for higher values. Finally, we show that bank profitability is a significant determinant of financial stability.