Various aspects of the improvement of the functioning of grinding accuracy are considered. Active methods of the control of grinding systems are proposed to ensure the quality required for finishing. It is pointed out that the quality of finishing is closely connected with the mutual position of the tool and the work piece in the grinding process. This position is appreciated by permissible state areas of the axis of the tool and the work piece. Analytical expression of this interaction is described by non-traditional mathematical model’s dependences. Mathematical models presented evaluate eccentricity between the tool and the work piece or between other elements of the system and enable one to better understand the appearance of the second and higher harmonics on the work piece processed or on the tool. They allow one to simulate the finishing not only of the cylindrical, but also of non-round profile work pieces, such as cams, eccentrics, etc. The mathematical dependences worked out allow one to build various modifications of the grinding systems and to evaluate the quality of their functioning. A circuit for the active control of the tool position is proposed, with the goal of quality improvement of finishing. For this purpose the usage of the adaptive spindle with tilting-pad journal bearings is suggested.