Arguments are summarized for why many of the best non‐qq candidates may be deuteronlike bound states of two vector mesons or KK*. Using pion exchange as a guide for where to look for bound states, only a few deuteronlike meson‐meson resonances are expected. Four of these are likely to be the already seen non‐qq candidates: f1(1420), f2(1520), f0(1590), f0(1710). In addition, one expects a K*0 (≊1660) composed of K*ω and K*ρ. In the charm sector one expects a D*D* composite χc0(≊4000) and an axial state DD* composite χc1 (≊3870). The last mentioned one implies a state doubling in the axial charm sector near 3900 MeV, similar to the f1(1420)−f1(1510) puzzle in the light quark sector. The second resonance is the expected cc23P1 χc1(≊3950). The χc1(≊3870) is particularly interesting, since it should be narrow and an almost unavoidable prediction of pion exchange. Namely, the exchanged pion can be almost on shell giving a Coulomb‐like potential, due to the mass relation mD*≊mD+mπ.