We present a new piece of evidence in favour of the importance of the
quark off-shellness in the kaon. The matrix elements of the flavour-ch
anging operators for K-L --> gamma gamma comply with the general behav
iour of the matrix elements expected in the pairing bound-state model
used here. The present calculation in essence agrees with previous chi
ral-quark results. The off-shell contribution turns out to be dominant
(the model on-shell amplitude being at the 10% level). Compared with
the chiral perturbation-theory approach, our off-shell contribution is
an entirely new O(p(4)) direct-decay piece, whereas the non-diagonal
magnetic-moment term belongs to the order O(p(6)).