Abstract: The existing theories of the crisis occurrence and contagion through the countries with different levels of economic development were examined in the work. There’s defined the object of study, revealed its characteristics and specified the requirements to the mathematical tools in the article. A correlation analysis of the classification characteristics was carried out in the study. Its results used for the pre-separation of the countries into classes. It was grounded the usage of neural networks for mathematical description of the cross-border contagion processes. Constructed the generalized diagram of models system for description the cross-border contagion between countries with different levels of socio-economic development based on chosen mathematical tools. At the first level of the system for splitting of countries into separate groups by type of response to the crisis phenomena is suggested to carry out their clustering using Kohonen maps. To predict the consequences of crisis transferring is decided to use the neural network of perceptron type at the system’s second level.