and masses, one can construct a Klein-Gordon system that is expected to blowup in finite time even for small data, on a heuristic level (though actually constructing blowup solutions would also be hard). On the other hand, for *generic* choices of speeds and masses, one has correct non-degeneracy and separation conditions (see [@DIP14]; see also [@DIPP16], [@G11] and [@GM11] for other models), and can still expect global well-posedness and scattering. See [@DIP14] for a system that exhibits the typical behavior for generic Klein-Gordon systems in two dimensions.

### Plan of this paper

In Section \[norms\] we define the relevant notations and in particular the $Z$ norm, and prove the crucial linear dispersion bound. In Section \[energy\] we prove the energy bound, and reduce Theorem \[mainkg\] to the main $Z$ norm estimate, namely Proposition \[main01\]. In Section \[beginning\] we make several reductions and get rid of some easy instances of Proposition \[main01\]; we then discuss the low frequency case in Section \[lowlowtolow\], and the medium frequency case, which requires more care, in Section \[med\]. The high frequency case is much easier and is dealt with in Section \[high\]. Finally, in Section \[phaseprop\] we collect some auxiliary facts about the phase function 