The importance of Born terms and resonance exchange for eta and eta' photop
roduction off both the proton and neutron within U(3) baryon chiral perturb
ation theory is investigated. Low-lying resonances such as the vector meson
s and J(P) = 1/2(+), 1/2(-) baryon resonances are included explicitly and t
heir contributions together with the Born terms are calculated. The couplin
g constants of the resonances are determined from strong and radiative deca
ys. We obtain reasonable agreement with experimental data near threshold.