[en] Pion-pion scattering is investigated in terms of the underlying quark dynamics. The wave function of an isolated pion, described as a quark-antiquark system interacting through a potential composed of a central and a spin-spin part, is determined using the spinless Salpeter equation. The kernel of the integro-differential equation governing the relative motion of the colliding pions is calculated using relativistic kinematics. The corresponding S- and D-wave pion-pion phase shifts and their Galilean counterparts are compared with experiment.