We present a GRANAT/SIGMA observation of the soft gamma-ray afterglow immed
iately after GRB 920723. The main burst is very bright. After similar to 6
s, the burst light curve makes a smooth transition into an afterglow where
flux decays as t(-0.7). The power-law decay lasts for at least 1000 s; beyo
nd this time, the afterglow emission is lost in the background fluctuations
. At least similar to 20% of main burst energy is emitted in the afterglow.
At approximately similar to 6 s after the trigger, we also observe an abru
pt change in the burst spectrum. At t < 6 s, the ratio of 8-20 and 75-200 k
eV fluxes corresponds to the power law spectral index alpha = 0.0-0.3. At t
= 6 s, the value of alpha increases to alpha approximate to 1 and stays at
this level afterwards. The observed afterglow characteristics are discusse
d in connection with the relativistic fireball model of gamma-ray bursts.