This paper develops a predator–prey model to explain cycles in credit-led economies. The predator is the part of the financial sector that issues credit money for non-output transactions. It increases the indebtedness ratio and inflates bubbles that eventually have a negative impact on the real rate of growth (the prey). From this basis, we build a couple of models that may lead to self-contained or explosive cycles. Even in the first case, there is a risk of a financial collapse when certain variables move far away from their long-term equilibrium positions. In order to tame the cycle and avoid extreme positions, governments should ban the expansion of credit money for the purchase of assets and introduce permanent checks to risky credit.