We present a new contribution to the K(L) --> gammagamma amplitude, wh
ich is O(p4) within the counting rules of chiral perturbation theory.
This direct (non-pole) amplitude, obtained from short-distance s --> d
gamma quark diagrams of order eG(F)alpha(s)/pi, and similar s --> dgam
magamma diagrams, can account for about half of the experimental ampli
tude. Closely following the description of the pi0 --> gammagamma and
K(L) --> gammagamma processes in the variants of the same low-energy Q
CD, we find that both of these processes are anomalous in the same sen
se. Then, by the anomaly-matching principle, we arrive from the chiral
-quark to the bosonic counterparts for both of these processes. In thi
s way we add the K(L) --> gammagamma decay to the existing list of ano
malous radiative prosesses.