Title: Mystery of Luminous Supersoft X-Ray Sources in Large Magellanic Cloud and Small Magellanic Cloud Author: A. Skopal Abstract: Luminous supersoft X-ray sources (SSSs) in LMC and SMC were discovered by the Einstein and ROSAT X-ray satellites in the 1980s and early 1990s. > From 1992 they are understood as close binary systems in which a massive white dwarf accretes from its companion generating luminosities of 10^36 - 2x10^38 erg/s. Applying own method of multiwavelength modeling the spectrum from supersoft X-rays to near-IR for the brightest SSSs in LMC and SMC revealed surprising results: (i) The luminosty of the brightest SSSs is of a few times 10^38 - 10^39 erg/s that is one order of magnitude above the Eddington limit, at which the radiation pressure balances the gravity, and (ii) the presence of a strong nebular emission dominating the spectrum from near-UV to longer wavelengths. I suggest that the brightest SSSs could be unidentified optical novae in a post-nova SSS state sustained at a high long-lasting luminosity by resumed accretion. Further investigation of these mysterious objects at all wavelengths will aid us in understanding their proper stage in stellar evolution.