Using a sample of 59 γ-ray-lound blazars with observed data of flux and spectral index in multiw avebands,we have studied the possible correlations of flux densities and the spectral index for different wavebands in low state. New possible constrains on the γ-ray emission is discussed from theory deeply. The results suggest that (1)the synchrotron self-Compton mechanism should be main responsible for the γ-ray f rom the blazars;(2)inverse Compton scattering of the radiation f rom ho t circumnuclear by beamed ult relativistic electrons is another important mechanism ;(3)BL Lac objects are not “pure nonthermal objects” and they are the thermal emit ting sources.
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