We investigate the continuum three-pion problem within a relativistic three-body model that takes into account the ππS andP waves. The dynamical input of the two-body subsystem is given by separable potentials, which yield a good fit to the ππ scattering data and resonance parameters up to a two-body invariant mass of 900MeV. We introduce a parameter ν expressing the ambiguity in the reduction of a fully relativistic theory to a three-dimensional one. The masses and widths of the ω,a1(1260), and π(1300) mesons, which decay predominantly into three pions, are reasonably well described by our model. Theh1(1170) meson, however, which also decays into three pions, cannot be explained as a three-pion resonance. Some πρ Argand diagrams are shown in those channels where resonances exist.