  Clusters of galaxies evolve and accrete mass, mostly from small galaxy
systems. Our aim is to study the velocity field of the galaxy cluster Abell
780, which is known for the powerful radio source Hydra A at its center and
where a spectacular X-ray tail associated with the galaxy LEDA 87445 has been
discovered. Our analysis is based on the new spectroscopic data for hundreds of
galaxies obtained with the Italian Telescopio Nazionale {\em Galileo} and the
Very Large Telescope. We have constructed a redshift catalog of 623 galaxies
and selected a sample of 126 cluster members. We analyze the internal structure
of the cluster using a number of techniques. We estimate the mean redshift
z=0.0545, the line-of-sight velocity dispersion sigmav about 800 km/s, and the
dynamical mass M200 about 5.4 10E14 solar masses. The global properties of
Abell 780 are typical of relaxed clusters. On a smaller scale, we can detect
the presence of a galaxy group associated with LEDA 87445 in projected phase
space. The mean velocity and position of the center of the group agree well
with the velocity and position of LEDA 87445. We estimate the following
parameters of the collision. The group is characterized by a higher velocity
relative to the main system. It is infalling at a rest frame velocity of
Vrf=+870 km/s and lies at a projected distance D=1.1 Mpc to the south, slightly
southeast of the cluster center. The mass ratio between the group and the
cluster is about 1:5. We also find evidence of an asymmetry in the velocity
distribution of galaxies in the inner cluster region, which might be related to
a small low-velocity group detected as a substructure at Vrf=-750 km/s. We
conclude that A780, although dynamically relaxed at first sight, contains small
substructures that may have some impact on the energetics of the core region.
