The Asal Ghoubbet rift in the Republic of Djibouti is a subaerial continuation of the Gulf of Aden ridge system. Many geological and tectonic arguments indicate that it represents one of the most typical spreading segments of the world rift system. Geodetic measurements regularly conducted from 1979 to 1983 across this area show an accumulation of extension in the inner floor of the rift valley with a rate of about 60 mm/yr perpendicular to the normal faults that bound the rift. Periodic leveling surveys across major faults in the rift show vertical creep movements of about 5 to 10 mm/yr. Although the observed deformations could be contaminated by postseismic relaxation after a rifting episode in November 1978, the regularity and the magnitude of these movements during the last two years argue for a steady state mechanism of deformation of the rift valley. The deformation is uniformly distributed in time and in space inside the inner floor of the rift. The necking of the lithosphere in the central part of the rift and the high temperature gradient imply a ductile rheology in the inner floor which is stretched in a steady state process.