  We investigate the X-ray origin in FRIs using the multi-waveband high
resolution data of eight FR I sources, which have very low Eddington ratios. We
fit their multi-waveband spectrum using a coupled accretion-jet model. We find
that X-ray emission in the source with the highest L_X (~1.8*10^-4 L_Edd) is
from the advection-dominated accretion flow (ADAF). Four sources with moderate
L_X(~several*10^-6 L_Edd) are complicated. The X-ray emission of one FR I is
from the jet, and the other three is from the sum of the jet and ADAF. The
X-ray emission in the three least luminous sources (L_X<1.0*10^-6L_Edd) is
dominated by the jet. These results roughly support the predictions of Yuan and
Cui(2005) where they predict that when the X-ray luminosity of the system is
below a critical value, the X-radiation will not be dominated by the emission
from the ADAF any longer, but by the jet. We also find that the accretion rates
in four sources must be higher than the Bondi rates, which implies that other
fuel supply (e.g., stellar winds) inside the Bondi radius should be important.
