Аннотация:Principles of classification of the systems of support of decision-making are analyzed. It offers to specify determination the "Intellectual decision-making support system". It is found out that existent classification of the systems of support of decision-making is inadequate to the real situation. It slows the process of creation and introduction in practical work of the systems of support of making decision. To such type it offers to take the systems, providing forming of managing influences in default of decision in existent terms. For providing of classification of the decision-making support systems the process of acceptance of administrative decisions is described in a formal kind. Concepts are entered "small" and "large" decision-making cycles. Within the framework of clarification of classification offered instead of the class used presently "in relation to an user level", to apply a class "on functional possibilities of the system", that will consist of the informative, calculation-informative and intellectual systems.