  This paper is concerned with the dynamical stability of the $N$-solitons of
the Benjamin-Ono (BO) equation. This extends the work of Neves and Lopes
\cite{LN} which was restricted to $N=2$ the double solitons case. By
constructing a suitable Lyapunov functional, it is found that the
multi-solitons are non-isolated constrained minimizers satisfying a suitable
variational nonlocal elliptic equation, the stability issue is reduced to the
spectral analysis of higher order nonlocal operators consist of the Hilbert
transform. Such operators are isoinertial and the negative eigenvalues of which
are located. Our approach in the spectral analysis consists in an invariant for
the multi-solitons and new operator identities motivated by the bi-Hamiltonian
structure of the BO equation. Since the BO equation is more likely a two
dimensional integrable system, its recursion operator is not explicit and which
contributes the main difficulties in our analysis. The key ingredient in the
spectral analysis is by employing the completeness in $L^2$ of the squared
eigenfunctions of the eigenvalue problem for the BO equation. It is
demonstrated here that orbital stability of soliton in $H^{\frac{1}{2}}(\R)$
implies that all $N$-solitons are dynamically stable in $H^{\frac{N}{2}}(\R)$.
