The notion of structural stability was introduced by Andronov and Pontriagin in 1937 for dynamic systems. Later on such a stability was established for various types of dynamic systems. Structural stability of control systems could be defined analogously but only here the point trajectory is the whole orbit of the point. Structural stability of generic control system on the closed oriented surfaces was established in beginning of 90-th of the last century (Davydov A.A., -{\sl Qualitative Theory of Control Systems}//Translations of Mathematical Monographs, Vol. 141, 1994, AMS, Providence, Rhode Island in cooperation with MIR, Moscow, 147 pp.) . The same question for generic dynamic inequalities is more difficult because, for example, the motion with limiting direction in such a case could include segments with sliding motion. The talk will be devoted to the recent results on the stability of generic dynamic inequalities with strictly convex sets of admissible velocities on oriented closed surfaces.