  Using HST images we have carried out a study of cluster populations in the
nearby S0 galaxy NGC 1023. In two WFPC2 pointings we have identified 221
cluster candidates. The small distance (~9 Mpc) combined with deep F555W and
F814W images allows us to reach about two magnitudes below the expected
turn-over of the globular cluster luminosity function. NGC 1023 appears to
contain at least three identifiable cluster populations: the brighter clusters
show a clearly bimodal color distribution with peaks at V-I = 0.92 and at V-I =
1.15 and in addition there are a number of fainter, more extended objects with
predominantly red colors. Among the brighter clusters, we find that the blue
clusters have somewhat larger sizes than the red ones with mean effective radii
of R(eff) ~ 2 and R(eff) ~ 1.7 pc, respectively. These clusters have luminosity
functions (LFs) and sizes consistent with what is observed for globular
clusters in other galaxies. Fitting Gaussians to the LFs of the blue and red
compact clusters we find turn-over magnitudes of M(TO,blue)=-7.58 and
M(TO,red)=-7.37 in V and dispersions of sigma(V,blue)=1.12 and
sigma(V,red)=0.97. The fainter, more extended clusters have effective radii up
to R(eff) ~ 10-15 pc and their LF appears to rise at least down to M(V) ~ -6,
few of them being brighter than M(V) = -7. We suggest that these fainter
objects may have a formation history distinct from that of the brighter GCs.
