I show that, in real small‐open as well as large‐open economies, international borrowing produces a destabilizing effect that significantly lowers the minimum level of increasing returns to scale needed for indeterminacy. In this case, a sufficiently high debt‐to‐capital ratio coefficient in the borrowing rate schedule operates like an automatic stabilizer that mitigates belief‐driven cyclical fluctuations. The analysis conducted within the monetary setting shows that both the benchmark nominal interest rate and the inflation rate of the country of the denominated currency may lessen the destabilizing effect of international borrowing. When domestic sunspot shocks exert sufficiently strong effects on these two variables, international borrowing may instead stabilize the domestic economy. I also find that inflation indexed bonds remove the stabilizing effect of the inflation rate of the country of the denominated currency and make different types of international bonds under different monetary regimes exhibit qualitatively the same destabilizing effect as real bonds in real economies. In addition, flexible inflation targeting performs no worse than rigid inflation targeting in all cases. Finally, the quantitative analysis undertaken shows that in the past few decades the considerable increase in foreign indebtedness may have destabilized the U.S. economy by giving rise to belief‐driven fluctuations.