In this paper we prove the existence of infinitely many distinct T-periodic solutions for the perturbed second order Hamiltonian system q + V 0(q) = f(t)under the conditions that V: RN→R is continuously differentiable and superquadratic, and that f is square integrable and T-periodic. In the proof we use the minimax method of the calculus of variation combining with a priori estimates on minimax values of the corresponding functionals.