Abstract: In this paper the symmetries of equations q_tt=g(q,q₁,q₂,…) are discussed, where q=q(x,t) and q_i=∂ⁱq/∂xⁱ. It is shown that if g=αq_s+g(q,…,q_r), α=const, s-r ≥ 2, then any symmetry of the equation will be linear with respect to the term of highest order. Furthermore, if the equation can be reduced to a Hamiltonian equation, then pairs of its conserved densities are in involution. As an application of this result, the Boussinesq equation q_tt=q₄+6q₁q₂+q₂ is shown to be a formal completely integrable Hamiltonian equation.