The paper contains a detailed analysis of the occurrence and contagion of crisis phenomena in countries with different levels of economic development. As part of the study, a correlation analysis of classification characteristics was carried out for the preliminary division of countries into classes. The usage of neural networks tools for the mathematical modelling of the processes of transboundary contagion of crisis is substantiated. A general scheme of the system of models of transboundary distribution of crisis phenomena between countries has been built. At the first level of the scheme for dividing countries into separate groups according to types of reaction to crisis phenomena, it was proposed to cluster them using self-organizing maps. At the second level of the scheme it was decided to use a perceptron-type neural network to predict the effects of crisis transfers.