The amplitude of the off-diagonal transition F(i) --> F(j)gamma*gamma* is calculated in the framework of the standard theory with fermion mixing assuming that m(ij)2, m(f)2, p1,2(2) << m(w)2. The expression obtained is applicable to the analyses of radiative and leptonic decays. of arbitrary spin K- and D-mesons. The result is employed to numerically estimate GAMMA(K(L)0 --> e+e-gamma)/GAMMA(K(L)0 ---> mu+mu-gamma).