  We construct a contact interaction model for the $\eta$ and $\eta'$ mesons in
the SDE-BSE approach to QCD and compute several static properties of these
mesons and their transition form factors. We find that this model gives an
excellent description of the $\eta$ and $\eta'$ static properties, namely their
masses, decay width and decay constants. However, a contact interaction
disagrees with experimental data for $Q^2$ greater than 2 GeV$^2$, and produces
transition form factors in conflict with perturbative QCD prediction. This is
not surpring and the reasons for this are explained
