The paper provides a forecast for the development of crisis phenomena in the economies of developed countries based on the modeling of N. Kondratiev’s cycles in the time series of real per capita GDP. To determine the dates of the beginning of the upward half-waves of the Kondratiev’s cycles, econometric models with a cyclic (harmonic) component were built. As a result of the study, it was found that the earliest manifestations of growth instability, the possibility of crisis phenomena in the economy are typical for the USA, Great Britain, and Italy. For most developed countries, the 2020s are the most likely opportunities for the development of crisis phenomena. Taking into account the possible reduction in the duration of Kondratiev’s cycles in post-industrial economic systems, a spectral analysis of quotations on the US stock market was performed, which showed a reduction in the duration of cycles to 40 years. The results obtained allow us to give the following estimate. For most developed countries, the most likely opportunities for the development of crisis phenomena are the 2010s and 2020s. Systemic crises in the economies of most developed countries can be expected in the 2020s and 2030s.