We consider scattering properties of the critical nonlinear system of wave equations with Hamilton structure
⎧uₜₜ - Δu = -F₁(|u|²,|v|²)u,
⎩vₜₜ - Δv = -F₂(|u|²,|v|²)v,
for which there exists a function F(λ,μ) such that
∂F(λ,μ)/∂λ = F₁(λ,μ), ∂F(λ,μ)/∂μ = F₂(λ,μ).
By using the energy-conservation law over the exterior of a truncated forward light cone and a dilation identity, we get a decay estimate for the potential energy. The resulting global-in-time estimates imply immediately the existence of the wave operators and the scattering operator.