The ESO Supernova Progenitor Survey (SPY) has identified 58 (mostly helium-rich) subluminous O stars. We use the Balmer line strength to distinguish sdO from He-sdO (no Balmer lines) and present the results of the analyses of high resolution optical VLT-UVES spectra using an extensive grid of NLTE atmosphere models covering a large range in Teff, log g and helium abundances. The stellar atmospheric parameters are derived from line profile fits using a chi**2 technique. The resulting distribution in the (Teff, log g) diagram as well as the luminosity function are discussed in the context of stellar evolution scenarios. By combining our results with those for the sdB stars from SPY (Lisker et al. 2004) we discuss the implications for binary population synthesis models of Han et al. (2003). Models with a low CEE efficiency and a constant mass ratio distribution provide a reasonable explanation of the observed properties of the SPY sample of sdB and sdO stars indicating that the sdO stars form the hot and luminous extension of the sdB sequence. However, for the He-sdO stars none of the considered evolution scenarios are in agreement with the measured parameters of our programme stars. We conclude that He-sdO stars are formed by a different process than the sdB and sdO stars.
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