A very large fraction of members of the class of X-ray sources called supersoft X-ray sources", initialy identified with ROSAT, are white dwarfs, accreting and burning hydrogen in shell in a close binary. More than 90 supersoft X-ray sources have been observed during the years in M31. About a third are post-outburst classical and recurrent novae, some are not interacting binaries, but there is evidence that at least 20% may be high mass X-ray binaries. Do they contain a whirte dwarf that is burning hydrogen in a shell, like their relatives in low mass X-ray binaries or CV-like systems? If this is the case, could they account for the prompt, star formation rate depending component of type Ia supernovae??