It is shown that the basic shape of dipion and KK̅ mass spectra in decays J/ψ→ϕ(ππ,KK̅), ψ (2S)→J/ψππ, Y(4260)→J/ψ π π and in the two-pion transitions of bottomonia states are explained by an unified mechanism based on the contribution ofthe ππ, KK̅ and η η coupled channels including their interference. The role of the individual f0 resonances in making up the shape of the dipion mass distributions in the charmonia and bottomonia decays is considered.