  We study orbital and physical properties of Trojan asteroids of Jupiter. We
try to discern all families previously discussed in literature, but we conclude
there is only one significant family among Trojans, namely the cluster around
asteroid (3548) Eurybates. It is the only cluster, which has all of the
following characteristics: (i) it is clearly concentrated in the proper-element
space; (ii) size-frequency distribution is different from background asteroids;
(iii) we have a reasonable collisional/dynamical model of the family.
Henceforth, we can consider it as a real collisional family.
  We also report a discovery of a possible family around the asteroid (4709)
Ennomos, composed mostly of small asteroids. The asteroid (4709) Ennomos is
known to have a very high albedo $p_V \simeq 0.15$, which may be related to a
hypothetical cratering event which exposed ice (Fern\'andez et al. 2003). The
relation between the collisional family and the exposed surface of the parent
body is a unique opportunity to study the physics of cratering events. However,
more data are needed to confirm the existence of this family and its
relationship with Ennomos.
