Jan Derezi/'n ski, Christian G{\'e}rard Long-range scattering in \\ the position representation (43K, LaTeX) ABSTRACT. For a large class of long-range potentials we prove the asymptotic completeness of modified wave operators constructed using solutions of the eikonal equation $-\p_t\Psi(t,x)=\12(\nabla_x\Psi(t,x))^2+V(x)$.