The method of classifying the typologies of money laundering and terrorist financing risks in big data from a variety of data sources of organizational systems is investigated. The main provisions of this technique are theoretically substantiated, reference models and calculation formulas are given. An algebraic approach for the synthesis of the method is proposed, a theoretical justification of the feasibility of its use is given. The algebraic approach to the synthesis of the methodology is implemented on the basis of category theory and the theory of algorithms, in particular the theory of Markov algorithms, which is considered outside of normal algorithms. The N-scheme of the Markov algorithm is considered, which was developed to replace its well-known g-scheme and provides processing of words in natural, artificial and combined languages, which can be represented in an ordered and extended Markov alphabet A±2, which takes into account many sources of big data. Methods for inputting incomplete, heterogeneous (heterogeneous) and non-representative input data samples are given. A method is proposed for converting input data samples into cycles of the Big Data Transfer Protocol. A reference model of the legal economic activity of the organizational system has been synthesized. This reference model is subjected to analysis and signs of illegal economic activity of mutually interacting organizational systems are highlighted. A reference model of the system for classifying the risks of laundering proceeds from crime and financing of terrorism has been developed. To combat money laundering, the N-scheme of the Markov algorithm for one data source and the Markov system, consisting of such schemes, for a variety of big data sources are theoretically substantiated. It is concluded that the synthesized Markov system provides a decomposition of words and their morphisms, contains a common data input control channel, and provides a classification of money laundering risks.