The first evidence for a differential rotation of the Earth's inner core wi
th respect to the mantle comes from the detection of a variation, over 30 y
ears, of the differential travel time anomalies of seismic core phases [Son
g, X., Richards, P.G., 1996. Seismological evidence for differential rotati
on of the Earth's inner core. Nature, 382, 221-224]. The comparison of tele
seismic doublets provides a powerful means to measure such differential tra
vel times and to test their temporal variation. Contrary to direct measurem
ents of differential travel times, this technique does not require to have
an accurate location of the seismic events. This method is first checked on
examples of doublers for which no differential travel time is expected. Th
ese tests allow us to point out the difficulties, such as polarity reversal
s, which may be encountered in the use of the doubler method. It is then ap
plied to deep Tonga events recorded in France and to the South Sandwich Isl
ands events recorded at station College (COL), Alaska, which led Song and R
ichards to propose an inner core rotation. For the first path, we find no t
ime variation, in agreement with previous studies. For the path from South
Sandwich Island to COL, the doubler analysis shows that no significant temp
oral change in PKP travel time can be detected within the resolution of the
method, which is about 0.05 s, The variation of the residuals observed by
Song and Richards, about 0.3 s over 30 years, is in a large extent ascribab
le to hypocenter mislocations. Consequently, present seismological observat
ions do not detect the inner core differential rotation because, if it exis
ts, it is smaller than about 0.2 degrees/year, the present detection capaci
ty of seismology. (C) 2000 Elsevier Science B.V. All rights reserved.