We present the results of our comparative timing and spectral analysis of t
he high and low (off) states in the X-ray pulsar Her X-1 based on data from
the ART-P telescope onboard the Granat observatory. A statistically signif
icant (several mCrab) persistent flux with a simple power-law spectrum was
detected during the low state. The spectral slope changed from observation
to observation by almost a factor of 2. Pulsations were detected only durin
g the high state of the source, when its flux was a factor of similar to 25
larger than the low-state flux. The spectral shape of Her X-1 in its high
state was complex, with the parameters depending on pulse phase. (C) 2000 M
AIK "Nauka/Interperiodica".