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\noindent We are exploring the evolution of stellar populations, on a time scale of 10 Myr, for a nuclear starburst occuring in the conditions similar to the Milky Way galaxy (evidence for a recent starburst at the Galactic center is summarized in $^1$). A computer code$^2$ is applied allowing for computing, by using Monte Carlo simulations, the evolution of a large ensemble of binary systems, with proper accounting for spin evolution of magnetized compact stars (white dwarfs and neutron stars). We are able to estimate the expected number of binary systems at different evolutionary stages of the starburst and to calculate the rate of some spectacular events such as the supernova rate, the binary neutron star coalescence rate, etc. Our results include the number of transients (NS + MS star), NS + supergiant, and BH + supergiant binaries, all as functions of time. The results are normalized so as to have the number of OB stars with masses greater than 10 $M_{\odot}$ to be consistent with the conclusion$^3$ that the age of the recent starburst at the Galactic center comprises 5-7 Myr. By this time, the majority of X-ray binaries is expected to be spread out to about 100 pc around the Galactic center. One of the results, which can be considered as a specific starburst feature, is that the ratio of the number of systems like SS 433 (BH or NS in the regime of superaccretion) to the number of transients is about 1:3, compared to 1:1000, characteristic to the average galactic field. The enhanced number of SS 433-like objects in the post-starburst regions might be associated with transient, stochasticaly oriented jets. \vskip 0.06truein \noindent $^1$ Ozernoy, L.M. 1994, in ``Multi-Wavelength Continuum Emission of AGN", eds. T.J.-L. Courvoisier \& A. Blecha, Kluwer, p. 351; \noindent $^2$ ``Scenario Machine" (see, e.g., Lipunov, V.M. et al. 1994, ApJ 423, L 121); \, \noindent $^3$~Tamblyn, P. \& Rieke, G.H. 1993, ApJ 414, 573
