Abstract. We characterize the Aubin property of canonically perturbed KKT system related to the second-order cone programming problem (SOCP) in terms of a strong second-order optimality condition. This condition requires the positive definiteness of a quadratic form, involving the Hessian of the Lagrangian and an extra term, associated with the curvature of the constraint set, over the linear space generated by the cone of critical directions. Since this condition is equivalent with the Robinson's strong regularity, the mentioned KKT system behaves (with some restrictions) similarly as in nonlinear programming.