This paper deals with variational inclusions of the form 0 ∈ φ(x) + F(x) where φ is a single-valued function admitting a second order Fréchet derivative and F is a set-valued map from ${ℝ}^q$ to the closed subsets of ${ℝ}^q$. When a solution z̅ of the previous inclusion satisfies some semistability properties, we obtain local superquadratic or cubic convergent sequences.