We examined X-ray, ultraviolet, and optical archival data of 89 supersoft X-ray sources (SSS) in M31. We studied the timescales of X-ray variability and searched UV and optical counterparts. Almost a third of the SSS are known classical or recurrent novae, and at least half of the others exhibit the same temporal behavior as post-outburst novae. Non-stellar objects among SSS seem to be rare: less than 10% of the classified SSS turned out to be supernova remnants, and only one source has been identified with an active galactic nucleus in the background. Not more than 20% of the SSS that are not coincident with observed novae are persistent or recurrent X-ray sources. A few of these long-lasting sources show characteristics in common with other SSS identified as white dwarf (WD) close binaries in the Magellanic Clouds and in the Galaxy, including variability on timescales of minutes, possibly indicating the spin period of a WD. Such objects are likely to be low-mass X-ray binaries with a massive WD. A third of the non-nova SSS are in regions of recent star formation, often at the position of an O or B star, and we suggest that they may be high-mass X-ray binaries. If these sources host a massive hydrogen-burning WD, as it seems likely, they may become Type Ia supernovae (SNe Ia), constituting the star formation dependent component of the SNe Ia rate.