We measure systemic risk in the network of financial market infrastructures (FMIs) as the probability that two or more FMIs have a large credit risk exposure to the same FMI participant. We construct indicators of credit risk exposures in three main Canadian FMIs during the period 2007–11 and use extreme value methods to estimate this probability. We find large differences in the contribution to systemic risk across participants. We also find that when participants are in financial distress, they tend to create large credit exposures in two or more FMIs. Our results suggest that an appropriate oversight of FMIs may benefit from an in-depth system-wide analysis, which may have useful implications for the macroprudential regulation of the financial system.