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Using published data, we have compiled the circular velocity (Vc) distribution function (VDF) of galaxy satellites in the Local Group. We find that within the volumes of radius of 570 kpc (400/h kpc for h=0.7) centered on the Milky Way and Andromeda, the average VDF is roughly approximated as n(>Vc)~ 45(Vc/10 km/s)^{-1} h^3 Mpc^{-3} for Vc in the range ~10-70 km/s. The observed VDF is compared with results of high-resolution cosmological simulations. We find that the VDF in models is very different from the observed one: n(>Vc)~1200(Vc/10 km/s)^{-2.75}h^3 Mpc^{-3}. Cosmological models thus predict that a halo of the size of our Galaxy should have about 50 dark matter satellites with circular velocity >20 km/s and mass >3x10^8/h Msun within a 570 kpc radius. This number is significantly higher than the approximate dozen satellites actually observed around our Galaxy. The observed and predicted VDFs cross at ~50 km/s, indicating that the predicted abundance of satellites with Vc> 50 km/s is in reasonably good agreement with observations. We conclude, therefore, that unless a large fraction of the Local Group satellites has been missed in observations, there is a dramatic discrepancy between observations and hierarchical models, regardless of the model parameters. We discuss several possible explanations for this discrepancy including identification of some satellites with the High Velocity Clouds observed in the Local Group, and the existence of dark satellites that failed to accrete gas and form stars due either to the expulsion of gas in the supernovae-driven winds or to gas heating by the intergalactic ionizing background. (Abridged)