Supersoft X-ray sources are a new class of luminous X-ray binaries discovered with the X-ray telescopes of the Einstein and ROSAT satellites and extensively studied in the optical with ground based telescopes, in the UV with IUE and HST and in X-rays with ROSAT, Beppo-SAX and ASCA (cf. Kahabka & van den Heuvel 1997, van Teeseling 1997). The luminosities derived for a first sample of supersoft sources studied with moderate resolution X-ray spectroscopy (using Beppo-SAX LECS and ASCA SIS detectors, Parmar et al. 1997, Ebisawa et al. 1997) have been predicted to follow Iben’s stability line (Iben 1982), i.e. the location in the Hertzsprung-Russell diagram which separates the plateau phase from the cooling phase. This is not unreasonable as any system experiencing steady-state accretion, i.e. accretion at a rate equalling about the nuclear burning rate will be found close to the stability line. If the accretion rate exceeds this limit then the white dwarf gets bloated and disappears in X-rays. If the accretion rate falls below this limit the white dwarf envelope cools, the luminosity as well as the temperature ceases and the source enters unstable recurrent nuclear burning. From the population synthesis calculations of Yungelson (1996) follows that there exit for the Milky Way a few sources at any epoch which are more massive than 1.2 MQ. They are expected to be extremely X-ray bright and may be standard candles (cf. Table 1 and Figure 1 for the brightest known supersoft sources per galaxy Milky Way to NGC 55). Their spectral distribution is expected to be similar to that of the extremely hot galactic source RXJ0925.7-4758 (it peaks at 1 keV and the flux is distributed from 0.5 to 2 keV, see Figure 2 for the ASCA spectrum of RX J0925.7-4758 (and CAL 87) as derived by Ebisawa et al. 1997).