  In this article we consider the three-particle decays $\chi_{b0,2}\to J/\psi
c\bar c\to J/\psi D\bar D+X$. We present the analytical formulae for the
differential widths of these decays, the numerical values of their integrated
widths and check the duality relation that connects the decays
$\chi_{b0,2}\to\psi c\bar c$ with the two-particle decays $\chi_{b0,2}\to
J/\psi (c\bar c)$. We also study the possibility of observing the
$\chi_{b0,2}\to J/\psi DD+X$ mode at Tevatron and LHC colliders.
