  We consider a nonlinear system of two-dimensional Klein-Gordon equations with
masses satisfying the resonance relation. We introduce a structural condition
on the nonlinearities under which the solution exists globally in time and
decays at the rate $O(|t|^{-1})$. In particular, our new condition includes the
Yukawa type interaction, which has been excluded from the null condition in the
sense of J.-M.Delort, D.Fang and R.Xue.
