Robert A. Karayev - Professor, Head of Ecosystems Modeling Laboratory, Institute of Control Systems of the Azerbaijan National Academy of Sciences Address: 9, B. Vahabzade Street, Baku, AZ1141, AzerbaijanE-mail: karayevr@rambler.ruRena N. Mikailova - Associate Professor, PhD in Economics, Azerbaijan State University of EconomicsAddress: 6, Istiqlaliyat Street, Baku, AZ1001, AzerbaijanE-mail: renam3@mail.ruIslam I. Safarly - PhD in Economics, Business Development Manager, OIL SUPPLY LLCAddress: 156, Batamdar Highway, Baku, AZ1006, AzerbaijanE-mail: islamsafarli@gmail.comNatella Y. Sadikhova - Researcher, Institute of Control Systems of the Azerbaijan National Academy of Sciences Address: 9, B. Vahabzade Street, Baku, AZ1141, AzerbaijanE-mail: natella5@rambler.ruXatire F. Imamverdiyeva - Software Engineer, Institute of Control Systems of the Azerbaijan National Academy of Sciences Address: 9, B. Vahabzade Street, Baku, AZ1141, AzerbaijanE-mail: imamverdiyeva.x@gmail.com The article discusses the difficulties of long-term dynamic analysis of business strategies of enterprises in present-day complex and unstable economic conditions. We discuss the possibility of solving the problem by means of cognitive modeling, which has opened a new page in the management of complex systems and complex problem situations. We note the phenomenological features of complex systems and complex problem situations that exclude the possibility of their modeling using traditional economic and mathematical methods. Such features are: multifactority, dynamism, uncertainty, the high role of the mentality of the developers of the strategy and the persons making strategic decisions. The urgency of the question of ensuring the reliability of cognitive models, a significant place in which is occupied by heuristic components, is emphasized. Formalization of the latter encounters numerous difficulties (“traps”) that arise at all stages of designing cognitive models - the stages of identification, conceptualization, formalization and testing, which constitute the specifics of the development of all knowledge-based support technologies. Existing methods and models from relevant areas that can be useful for overcoming these difficulties are considered (strategic analysis, strategic planning, scenario analysis, scenario planning, SWOT analysis, PEST analysis, SMART technology, methods of knowledge identification, methods of psycho semantics and non-metric multidimensional scaling, methods of expert evaluation). The article presents a demo version of cognitive tools for dynamic analysis of strategies (cognitive map of strategy and cognitive map analysis methods), based on the ideology of cognitive modeling. Consideration is given to the application possibilities of cognitive tools in the analysis of strategies in the context of possible dynamics of the internal and external environment of the enterprise. An example of the use of cognitive tools is given.This work was supported by the Foundation for Science Development under the President of the Azerbaijan Republic (grant No. EİF-KETPL-2-2015-1(25)-56/14/1)