The systematization of physical flow models at the peripheral region of the rotors of axial compressor is carried out. Based on the experimental and numerical studies, the flow features in subsonic and transonic rotors are analyzed. Similar features of the flow near the wall at the periphery of subsonic and transonic rotors are formulated. The characteristic areas and individual features of the near-wall flow in them, which are obtained in experimental studies of the flow structure at the periphery of the blade rows, are reflected. The analysis of the influence of annular grooves in the axial compressor case on the flow in the airfoil channel of the subsonic and transonic rotors is presented. The hypothetical mechanism of the flow effect in the cavity of the annular groove on the main flow at the tip region of the airfoil channel of axial compressor rotor is described. An approach to generalize the experimental data of the axial compressor stages with the casing treatment based on the selected fundamental system of dimensionless parameters characterizing the main features of the flow at the rotor tip region are proposed. Using the approach, the dependences of the casing treatment effect on the gas-dynamic stability limit and efficiency are obtained. It was found, when Reynolds numbers ReΔr> 400 increase, the efficiency of annular groove casing treatment in the axial compressor wall on the gas-dynamic stability limit of the compressor decreases. The existence of the region of aerodynamic efficiency modes of the annular groove casing treatment in the case is shown. In this area, there is an optimal mode when the maximum effect of efficiency from install annular groove casing treatment is achieved. The obtained generalization al-lows us, at the step of making design decisions, to evaluate the effectiveness of the annular groove casing treatment in the case when it is used in subsonic and transonic rotors of the axial compressor stages.