  The Crab Nebula and the Pulsar have been pointed several times by the
BeppoSAX satellite. We analysed all these observations, summed together, to
study the main spectral properties with a good phase resolution. A new accurate
estimate of the hydrogen column density in the Crab direction N_H=3.23 x
10^(21) cm^(-2) is given as derived from the analysis of the off-pulse emission
at low energies. We studied the changes of the spectral index with the pulse
phase and showed that in the interpeak region it is systematically harder than
in the main peaks of about 0.4. We observed also a significant spectral
steepening of the pulsed emission and showed that this distribution can be
represented by a unique law with a linear variable log slope and apply it to
the spectrum of the first peak. A two component model is proposed to explain
the phase evolution of the spectrum. One component has the same profile
observed in the optical while the other presents a maximum at the phase 0.4
with essentially the spectrum of the interpeak region. Two possible
interpretations for the origin of the latter component are discussed.
