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Within the OPE, we the new sum rules in Heavy Quark Effective Theory in theheavy quark limit and at order 1/m_Q, using the non-forward amplitude. Inparticular, we obtain new sum rules involving the elastic subleading formfactors chi_i(w) (i = 1,2, 3) at order 1/m_Q that originate from the L_kin andL_mag perturbations of the Lagrangian. To the sum rules contribute only thesame intermediate states (j^P, J^P) = ((1/2)^-, 1^-), ((3/2)^-, 1^-) that enterin the 1/m_Q^2 corrections of the axial form factor h_(A_1)(w) at zero recoil.This allows to obtain a lower bound on -delta_(1/m^2)^(A_1) in terms of thechi_i(w) and the shape of the elastic IW function xi(w). An importanttheoretical implication is that chi'_1(1), chi_2(1) and chi'_3(1) (chi_1(1) =chi_3(1) = 0 from Luke theorem) must vanish when the slope and the curvatureattain their lowest values rho^2->3/4, sigma^2->15/16. These constraints shouldbe taken into account in the exclusive determination of |V_(cb)|.Comment: Invited talk to the International Workshop on Quantum Chromodynamics  : Theory and Experiment, Conversano (Bari, Italy), 16-20 June 200

Sum Rules for Leading and Subleading Form Factors in Heavy Quark Effective Theory using the Non-forward Amplitude