This paper examines the impact of market competition on the stability of Islamic and conventional banks in countries where these banks operate alongside one another. To investigate this issue, we use a sample of 100 Islamic and 390 conventional banks from 19 countries. Our baseline result shows that competition in a dual market erodes banks' stability. The heightened competitive pressure in a dual market encourages banks to engage in excessive risk-taking that can jeopardize their stability. However, the effect of competition is missing for Islamic banks, suggesting their superiority in having religious clients. Although our overall results support the 'competition-fragility' hypothesis, we find that competition can be beneficial for banks, especially at a low to medium competition level. Last, we also find that the adverse impact of competition can be reduced by having high capitalization, especially in the case of a conventional bank. Some policy implications are discussed in the paper.