Risk Management is one of the important functional areas in the project management methodology. In practice, as a rule, qualitative risk assessments are applied. However, the theory of risk management based on qualitative assessments is virtually absent. The article attempts to present the elements of risk management theory based on qualitative assessments. The definition of qualitative assessments of complex risks is given. The tasks of risk management (by reducing them, evasion) are set. Algorithms for solving the corresponding problems are proposed.