  Asteroid families are formed as the result of collisions. Large fragments are
ejected with speeds of the order of the escape velocity from the parent body.
After the family formation, the fragments' orbits evolve in the space of proper
elements because of gravitational and non-gravitational perturbations, such as
the Yarkovsky effect. Disentangling the contribution to the current orbital
position of family members caused by the initial ejection velocity field and
the subsequent orbital evolution is usually a difficult task. Among the more
than 100 asteroid families currently known, some interact with secular
resonances. Linear secular resonances occur when there is a commensurability
between the precession frequency of the longitude of the pericenter (g) or of
the longitude of node (s) of an asteroid and a planet, or a massive asteroid.
The linear secular resonance most effective in increasing an asteroid
eccentricity is the ${\nu}_6$, that corresponds to a commensurability between
the precession frequency g of an asteroid and Saturn's $g_6$. Non-linear
secular resonances involve commensurabilities of higher order, and can often be
expressed as combinations of linear secular resonances. This is the case, for
instance, of the $z_k=k(g-g_6)+(s-s_6)$ resonances. Asteroid families that are
crossed by secular resonances are of particular interest in dynamical
astronomy. First, they often provide a clear evidence of asteroid orbit
evolution due to the Yarkovsky effect. Second, conserved quantities of secular
dynamics can be used to set valuable constraints on the magnitude of the
original ejection velocity field. Finally, by changing the value of inclination
of family members nodal secular resonances with massive asteroids or dwarf
planets can cause the i distribution to become more and more leptokurtic (i.e.,
more peaked and with larger tails than that of a Gaussian distribution).
