************************************************************************* 51049 Supersoft X-ray source (SSS) is a new class of binary X-ray sources detected by Einstein and ROSAT in nearby galaxies. Such sources radiate near the Eddington limit of a 1 solar mass compact object with blackbody temperatures of 10 to 60 eV. Models for the SSS are accreting black holes or neutron stars with an extended scattering cloud maintained by super Eddington accretion and a white dwarf (WD) in a close binary system a ccreting at high rates with steady nuclear burning. High resolution spectroscopic observations by ASCA can identify the plausible model and can uncover the compact source in the SSS. *************************************************************************