  The Energetic Gamma-Ray Experiment Telescope (EGRET) on the Compton Gamma-Ray
Observatory (CGRO) discovered gamma-ray emission from more than 67 blazars
during its 9 yr lifetime. We conducted an exhaustive search of the EGRET
archives and selected all the blazars that were observed multiple times and
were bright enough to enable a spectral analysis using standard power-law
models. The sample consists of 18 flat-spectrum radio quasars(FSRQs), 6
low-frequency peaked BL Lac objects (LBLs) and 2 high-frequency peaked BL Lac
objects (HBLs). We do not detect any clear pattern in the variation of spectral
index with flux. Some of the blazars do not show any statistical evidence for
spectral variability. The spectrum hardens with increasing flux in a few cases.
There is also evidence for a flux-hardness anticorrelation at low fluxes in
five blazars. The well-observed blazars (3C 279, 3C 273, PKS 0528+134, PKS
1622-297 PKS 0208-512) do not show any overall trend in the long-term spectral
dependence on flux, but the sample shows a mixture of hard and soft states. We
observed a previously unreported spectral hysteresis at weekly timescales in
all three FSRQs for which data from flares lasting for ~(3-4) weeks were
available. All three sources show a counterclockwise rotation, despite the
widely different flux profiles. We analyze the observed spectral behavior in
the context of various inverse Compton mechanisms believed to be responsible
for emission in the EGRET energy range. Our analysis uses the EGRET skymaps
that were regenerated to include the changes in performance during the mission.
