************************************************************************* 62142 The different spectral properties of blazar subclasses provide important clues about the nature of these objects. The steep X-ray spectra of High-energy peaked BL Lacs, together with their flat values of the radio-to-X-ray indices, alpha-rx, indicate that these objects are synchrotron-dominated, while inverse Compton emission plays a more important role in Low-energy peaked BL Lacs and FSRQs as indicated by their flat X-ray continua and steep alpha-rx indices. We have found a new FSRQ subclass with unexpectedly steep ROSAT spectra (photon index > 2) and alpha-rx intermediate between HBLs and LBLs. We propose to observe with ASCA the 7 brightest steep X-ray FSRQs to determine the shape of their high-energy continua for the first time and clarify their role in the blazar family. *************************************************************************