Abstract: Several dispersive wave equations can be formulated as Hamiltonian PDEs.  Steady travelling waves can then be interpreted as critical points of the Hamiltonian functional.  Furthermore, their stability is linked to the spectrum of the Hessian of this functional.  In this talk, the Maslov index, an index defined on paths of Lagrangian spaces, is used to study this spectrum in the case of traveling waves arising in various higher-order Korteweg-de Vries-type equations.