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For the heavy quarkonium system we examine ${\cal O}(\Lambda_{\rm QCD}^2/m)$renormalons, which are expected to be included in the perturbative series ofthe pole mass and $1/(mr^2)$ interquark potential. We find indications ofexistence and cancellation of these renormalons, from examinations of stabilityand convergence properties of the perturbative series and their resummations,as well as by comparison with the known properties of the ${\calO}(\Lambda_{\rm QCD})$ renormalons.

On order $\Lambda_{\rm QCD}^2/m$ renormalons in quarkonium system