Abstract Note: Human activity can create or mitigate risks of catastrophes, such as nuclear war, climate change, pandemics, or artiﬁcial intelligence run amok. These could even imperil the survival of human civilization. What is the relationship between economic growth and such existential risks? In a model of directed technical change, with moderate parameters, existential risk follows a Kuznets-style inverted U-shape. This suggests we could be living in a unique “time of perils,” having developed technologies advanced enough to threaten our permanent destruction, but not having grown wealthy enough yet to be willing to spend suﬃciently on safety. Accelerating growth during this “time of perils” initially increases risk, but improves the chances of humanity’s survival in the long run. Conversely, even short-term stagnation could substantially curtail the future of humanity.