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\noindent Supersoft X-ray sources, originally discovered with the Einstein observatory\negthinspace $^{[1]}$, have now been established as an important new class of X-ray source in the Rosat all-sky survey. These objects have characteristic luminosities of $\sim 10^{38}$ ergs s$^{-1}$ and effective temperatures of $\sim 4 \times 10^5$ K ($k T \sim 35$ eV), about a factor of 100 times lower than $kT$ for more conventional X-ray binaries. The known supersoft sources include 5 in the LMC, 4 in the SMC, 2 in our Galaxy, 8 in M31, 1 in NGC 253 and 1 in M101$^{[2]}$. Two of the supersoft sources have been identified with optical counterparts in the LMC, having orbital periods of 10.6 hours and 1.04 days. A particular model for these systems invokes steady nuclear burning of accreted matter on the surface of a $\sim 1 M_{\odot}$ white dwarf from a main-sequence or subgiant companion star of $\sim 1.5-2 M_{\odot}$\negthinspace $^{[3]}$. Mass transfer rates of between 1 and 4 $\times 10^{-7} M_{\odot}$ yr$^{-1}$ are required to sustain the observed luminosities. Such high transfer rates are a natural consequence of unstable mass transfer on a thermal time scale via Roche lobe overflow in this type of system.
\noindent We present the results of a Monte Carlo simulation of the formation and evolution of such systems. Distributions of expected orbital periods, luminosities, effective temperatures, white dwarf masses, and companion masses are presented. We find that there should be on the order of $10^{3}$ such systems in the Galaxy and in M31, and that the orbital periods should lie in the range of 10 hours to 4 days. We demonstrate why these sources should be easier to detect in nearby external galaxies at relatively high galactic latitude than they are in the plane of our own Galaxy.\hfil\break
\noindent $^1$ Long, K., Helfand, D., \& Grabelsky, D. 1981, Ap.J., 248, 925.\hfil\break \noindent $^2$ Tr\"umper, J. 1993, private communication.\hfil\break \noindent $^3$ van den Heuvel, E.P.J., Bhattacharya, D., Nomoto, K., \& Rappaport, \hfil\break \vrule height 0pt depth 0pt width .8cm S.A. 1992, A\&A, 262, 47.\hfil\break
