Absract. The approach proposed in the paper represents financial-economic systems with one input and one output through the optimal singular adaptive M3A1N computer observer as an arbitrary limited set of discrete linearized observable submodels with unknown parameters, unknown initial vector of the endogenous state variables and unknown current state vector of the endogenous state variables. The synthesis of the adaptive M3A1N algorithm is carried out with the help of the toolbox of the Theory of Optimal Singular Adaptive (OSA) Computer Observation and Modeling which has been worked out by the authors in the last 27 years at Varna Technical University.