  GRB 020124 and GRB 030323 constitute half the sample of gamma-ray bursts with
a measured redshift greater than 3. This paper presents the temporal and
spectral properties of these two gamma-ray bursts detected and localized with
HETE-2. While they have nearly identical redshifts (z=3.20 for GRB 020124, and
z=3.37 for GRB 030323), these two GRBs span about an order of magnitude in
fluence, thus sampling distinct regions of the GRB luminosity function. The
properties of these two bursts are compared with those of the bulk of the GRB
population detected by HETE-2. We also discuss the energetics of GRB 020124 and
GRB 030323 and show that they are compatible with the Epeak - Eiso relation
discovered by Amati et al. (2002). Finally, we compute the maximum redshifts at
which these bursts could have been detected by HETE-2 and we address various
issues connected with the detection and localization of high-z GRBs.
