  Simultaneous observations of the accretion-powered millisecond pulsar IGR
J00291+5934 by International Gamma-Ray Astrophysics Laboratory and Rossi X-ray
Timing Explorer during the 2004 December outburst are analysed. The average
spectrum is well described by thermal Comptonization with an electron
temperature of 50 keV and Thomson optical depth tau_T ~ 1 in a slab geometry.
The spectral shape is almost constant during the outburst. We detect a spin-up
of the pulsar with nudot=8.4x10E-13 Hz/s. The ISGRI data reveal the pulsation
of X-rays at a period of 1.67 milliseconds up to ~150 keV. The pulsed fraction
is shown to increase from 6 per cent at 6 keV to 12--20 per cent at 100 keV.
This is naturally explained by the action of the Doppler effect the
exponentially cutoff Comptonization spectrum from the hot spot. The nearly
sinusoidal pulses show soft lags with complex energy dependence, increasing up
to 7 keV, then decreasing to 15 keV, and seemingly saturating at higher
energies.
