  The Lyapunov stability is established for the N-soliton solutions in the Lax
hierarchy of the Benjamin-Ono (BO) equation. We characterize the N-soliton
profiles as critical points of certain Lyapunov functional. By using several
results derived by the inverse scattering transform of the BO equation, we
demonstarate the convexity of the Lyapunov functional when evaluated at the
N-soliton profiles. From this fact, we deduce that the N-soliton solutions are
energetically stable.
