  Two-pion transitions in charmonium and bottomonium are considered with the
leading relativistic effects taken into account. The contribution of the
chromo- magnetic interaction of the charmed quarks to the amplitude of the
decay $\psi(2S) \to \pi \pi J/\psi$ is estimated from the available data. This
contribution is enhanced by a factor of three in the decay $\eta_c(2S) \to \pi
\pi \eta_c$ and should produce a noticeable modification of the rate and the
spectrum in the latter decay. It is argued that the peculiar observed spectrum
in the decay $\Upsilon(3S) \to \pi \pi \Upsilon$ arises due to a dynamical
suppression of the leading nonrelativistic quarkonium amplitude and thus
enhanced prominence of the relativistic terms. Also discussed are the effects
of the final state interaction between the pions.
