We present a covariant approach to describe the low‐lying scalar, pseudoscalar, vector and axialvector mesons as quark‐antiquark bound states. This approach is based on an effective interaction modeling of the non‐perturbative structure of the gluon propagator that enters the quark Schwinger‐Dyson and meson Bethe‐Salpeter equations. We extract the meson masses and compute the pion and kaon decay constants. We obtain a quantitatively correct description for pions, kaons and vector mesons while the calculated spectra of scalar and axialvector mesons suggest that their structure is more complex than being quark‐antiquark bound states. © 2003 American Institute of Physics