  We present a precise optical and near-infrared determination of the Tip of
the Red Giant Branch (TRGB) brightness in the Large and Small Magellanic Clouds
(respectively LMC and SMC). The commonly used calibrations of the absolute
magnitude of the TRGB lead to an overestimation of the distance to the LMC and
SMC in the K band, and an underestimation of the distance in the optical I band
for both galaxies. Reported discrepancies are at the level of 0.2 mag, with
respect to the very accurate distance determinations to both Clouds based on
late-type eclipsing binaries. The differential distances between the LMC and
SMC obtained in the J and K bands, and for the bolometric brightness are
consistent with each other, and with the results obtained from eclipsing
binaries and other distance indicators.
