The author analyzes the principles and the methodological grounds for a dynamics approach to modeling political stability, regarding stability and crisis as a process and accentuating structural characteristics of the system being changed with time. It is noted that in modern political science the main direction of the development of a dynamics approach of analyzing stability is systemic dynamic modelling (SDM). As the key problem of developing modern systemic dynamics, the author points to extraordinary and redundant complication of, whereas, in his opinion, it is only comparatively simple mathematical models that are capable of working.