  We studied the evolution of the X-ray and gamma-ray spectra of the Crab
pulsar utilizing the 11-year observations from the Rossi X-ray Timing Explorer
(RXTE) and 9-year observations from the Fermi Gamma-ray Space Telescope (FGST).
By fitting the spectrum of each observation, we obtained the corresponding
flux, and then analysed the long term evolution of the X-ray (or gamma-ray)
luminosities as well as their correlations with the spin down power of the
pulsar. The X-ray flux in 5-60 keV obtained by the Proportional Counter Array
(PCA) of RXTE decreases with a rate of (-2.4+/-0.4)*10^(-14) erg cm^(-2) s^(-1)
per day. The X-ray flux in 15-250 keV obtained by the High Energy X-ray Timing
Experiment (HEXTE) of RXTE and the gamma-ray flux in 0.1-300 GeV by the Large
Area Telescope (LAT) onboard FGST show similar decreasing trend, but are
unsignificant statistically. The 5--60 keV X-ray luminosity L_(X) is correlated
with the spin down power L_(sd) by L_(X) propto L_(sd)^(1.6+/-0.3), which is
similar to the statistical results for young pulsars.
