  The dispersive two-photon contribution to the K_L --> mu+ mu- decay amplitude
is analyzed, using chiral perturbation theory techniques and large-N_C
considerations. A consistent description of the decays Pi^0 --> e+ e-, Eta -->
mu+ mu- and K_L --> mu+ mu- is obtained. As a byproduct, one predicts Br(Eta
--> e+ e-) = (5.8+-0.2) x 10^-9 and Br(K_L --> e+ e-) = (9.0+-0.4) x 10^-12.
