Low‐energy meson‐meson scattering data are a powerful testing ground for quark models. Here, we describe the behaviour at threshold ofS‐wave scattering‐matrix singularities. The majority of the full scattering‐matrix mesonic poles stem from an underlying confinement spectrum. However, the light scalar mesonsK0*(830),a0(980),f0(400–1200), andf0(980) do not, but instead originate in3P0‐barrier semi‐bound states. We show that the behaviour of the corresponding poles is identical at threshold. In passing, the light‐meson sector is given a firm basis. © 2003 American Institute of Physics