  We present distance determinations for two Local Group dwarf spheroidal
galaxies, Carina and Fornax, based on the near-infrared magnitudes of the tip
of the red giant branch (TRGB). For Carina we derive true distance moduli of
20.09 and 20.13 mag in the J and K bands, respectively, while for Fornax the
same distance modulus of 20.84 mag was derived in both filters. The statistical
errors of these determinations are of order 0.03-0.04 mag, whereas the
systematic uncertainties on the distances are 0.12 mag in the J band and 0.14
mag in the K band. The distances obtained from the near-infrared TRGB method in
this paper agree very well with those obtained for these two galaxies from
optical calibrations of the TRGB method, their horizontal branches, RR Lyrae
variables, and the near-infrared magnitudes of their red clumps.
