  Current amount of ~500 asteroid models derived from the disk-integrated
photometry by the lightcurve inversion method allows us to study not only the
spin-vector properties of the whole population of MBAs, but also of several
individual collisional families. We create a data set of 152 asteroids that
were identified by the HCM method as members of ten collisional families, among
them are 31 newly derived unique models and 24 new models with well-constrained
pole-ecliptic latitudes of the spin axes. The remaining models are adopted from
the DAMIT database or the literature. We revise the preliminary family
membership identification by the HCM method according to several additional
criteria - taxonomic type, color, albedo, maximum Yarkovsky semi-major axis
drift and the consistency with the size-frequency distribution of each family,
and consequently we remove interlopers. We then present the spin-vector
distributions for eight asteroidal families. We use a combined orbital- and
spin-evolution model to explain the observed spin-vector properties of objects
among collisional families. In general, we observe for studied families similar
trends in the (a_p, \beta) space: (i) larger asteroids are situated in the
proximity of the center of the family; (ii) asteroids with \beta>0{\deg} are
usually found to the right from the family center; (iii) on the other hand,
asteroids with \beta<0{\deg} to the left from the center; (iv) majority of
asteroids have large pole-ecliptic latitudes (|\beta|\gtrsim 30{\deg}); and
finally (v) some families have a statistically significant excess of asteroids
with \beta>0{\deg} or \beta<0{\deg}. Our numerical simulation of the long-term
evolution of a collisional family is capable of reproducing well the observed
spin-vector properties. Using this simulation, we also independently constrain
the age of families Flora (1.0\pm0.5 Gyr) and Koronis (2.5-4 Gyr).
