According to the hierarchical clustering scenario, galaxies are assembled b
y merging and accretion of numerous satellites of different sizes and masse
s. This ongoing process is not 100% efficient in destroying all of the accr
eted satellites, as evidenced by the satellites of our Galaxy and of M31. U
sing published data, we have compiled the circular velocity (V-circ) distri
bution function (VDF) of galaxy satellites in the Local Group. We find that
within the volumes of radius of 570 kpc (400 h(-1) kpc assuming the Hubble
constant(1) h = 0.7) centered on the Milky Way and Andromeda, the average
VDF is roughly approximated as n(> V-circ) approximate to 55 +/- 11(V-circ/
10 km s(-1))(-1.4+/-0.4) h(3) Mpc(-3) for V-circ in the range approximate t
o 10-70 km s(-1) The observed VDF is compared with results of high-resoluti
on cosmological simulations. We find that the VDF in models is very differe
nt from the observed one: n(> V-circ) approximate to 1200(V-circ/10 km s(-1
))(-2.75) h(3) Mpc(-3). Cosmological models thus predict that a halo the si
ze of our Galaxy should have about 50 dark matter satellites with circular
velocity greater than 20 km s(-1) and mass greater than 3 x 10(8) M., withi
n a 570 kpc radius. This number is significantly higher than the approximat
ely dozen satellites actually observed around our Galaxy. The difference is
even larger if we consider the abundance of satellites in simulated galaxy
groups similar to the Local Group. The models predict similar to 300 satel
lites inside a 1.5 Mpc radius, while only similar to 40 satellites are obse
rved in the Local Group. The observed and predicted VDFs cross at approxima
te to 50 km s(-1), indicating that the predicted abundance of satellites wi
th V-circ greater than or similar to 50 km s(-1) is in reasonably good agre
ement with observations. We conclude, therefore, that unless a large fracti
on of the Local Group satellites has been missed in observations, there is
a dramatic discrepancy between observations and hierarchical models, regard
less 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 satel
lites that failed to accrete gas and form stars either because of the expul
sion of gas in the supernovae-driven winds or because of gas heating by the
intergalactic ionizing background.