  We present Atacama Large Millimiter/submillimiter Array (ALMA) observations
of eight highly excited CO (J$_{\rm up}>8$) lines and continuum emission in two
$z\sim6$ quasars: SDSS J231038.88+185519.7 (hereafter J2310), for which
CO(8-7), CO(9-8), and CO(17-16) lines have been observed, and ULAS
J131911.29+095951.4 (J1319), observed in the CO(14-13), CO(17-16) and CO(19-18)
lines. The continuum emission of both quasars arises from a compact region ($<
0.9$ kpc). By assuming a modified black-body law, we estimate dust masses of
Log$(M_{\rm dust}/M_{\odot})=8.75\pm0.07$ and Log$(M_{\rm
dust}/M_{\odot})=8.8\pm0.2$ and dust temperatures of $T_{\rm dust}=76\pm3~{\rm
K}$ and $T_{\rm dust}=66^{+15}_{-10}~{\rm K}$, respectively for J2310 and
J1319. Only CO(8-7) and CO(9-8) in J2310 are detected, while $3\sigma$ upper
limits on luminosities are reported for the other lines of both quasars. The CO
line luminosities and upper limits measured in J2310 and J1319 are consistent
with those observed in local AGN and starburst galaxies, and other $z\sim 6$
quasars, except for SDSS J1148+5251 (J1148), the only quasar at $z=6.4$ with a
previous CO(17-16) line detection. By computing the CO SLEDs normalised to the
CO(6-5) line and FIR luminosities for J2310, J1319, and J1149, we conclude that
different gas heating mechanisms (X-ray radiation and/or shocks) may explain
the different CO luminosities observed in these $z\sim6$ quasar. Future J$_{\rm
up}>8$ CO observations will be crucial to understand the processes responsible
for molecular gas excitation in luminous high-$z$ quasars.
