We present data for 18 blazars observed with the X-ray satellite ASCA, half of which were also observed contemporaneously with the EGRET instrument onboard Compton Gamma-ray Observatory as parts of multi-wavelength campaigns. The observations show a clear difference in the spectra between three subclasses of blazars, namely the High-energy peaked BL Lac objects (HBLs), Low-energy peaked BL Lac objects (LBLs), and quasar-hosted blazars (QHBs). The ASCA X-ray spectra of HBLs are the softest, with the power law energy index α ∼ 1 − 2, and they form the highest observable energy tail of the low energy (LE, synchrotron) component. The X-ray spectra of the QHBs are the hardest (α ∼ 0.6) and are consistent with the lowest observable energy end of the high energy (HE, Compton) component. For LBLs, the X-ray spectra are intermediate. We find that the radiation process responsible for the HE peak for HBLs can be explained solely by Doppler-boosted Synchrotron-Self-Compton (SSC) emission, with the Doppler factor δ consistent with the VLBI and/or γ-ray variability data. For many QHBs, on the other hand, the γ-rays cannot be solely due to the SSC mechanism unless δ is significantly in excess of that inferred from VLBI data. We consider an alternative scenario consistent with the measured values of δ, where the SSC component is still present in QHBs and it dominates in the X-ray band, but it is below the observed γ-ray spectrum. With an assumption that the peak of the SSC emission is on the extrapolation of the X-ray spectrum, and adopting δ of 10, we infer the magnetic field B to be 0.1 -1 Gauss, and Lorentz factors γ b of electrons radiating at the peak of the νF (ν) spectrum of ∼ 10 3 for QHBs; this is much lower than γ b ∼ 10 5 for HBLs, even though the values of B are comparable in the two sub-classes. This difference of γ b is most likely due to the large photon density expected in QHBs (e.g. from thermal components visible in these objects) as compared with that of HBLs; Compton upscattering of these photons may well provide the observed GeV flux.