  We present a calculation of $P\to \gamma^{(\ast)}\gamma^{(\ast)}$ processes,
where $P=\pi^0,\ \eta,\ \eta'$, at the one-loop level up to and including
next-to-next-to-leading order (NNLO) in large-$N_c$ chiral perturbation theory.
The results are numerically evaluated successively at LO, NLO, and NNLO. The
appearing low-energy constants are determined through fits to the available
experimental data. We investigate the decay widths to real photons, the
single-virtual transition form factors, and the widths of $P\to\gamma l^+l^-$,
where $l=e,\ \mu$. Furthermore, we provide results for the slopes and
curvatures of the transition form factors.
