We consider the contributions of the C-odd axial-vector resonances (b1,h1) to eta-->pi0gammagamma, as well as those of the usual C-odd vector resonances (rho,omega) and chiral loops. Inclusion of b1(1235), h1(1170), h1(1380) increases the decay width of eta-->pi0gammagamma, improving the theoretical prediction. The measurement of the gammagamma spectrum can test our model. We also discuss the effects of these C-odd axial-vector resonances on electromagnetic interactions of neutral pions: gammagamma-->pi0pi0 and electric and magnetic polarizabilities of pi0.