  We aim to obtain new insights into the internal dynamics of the cluster Abell
2345. This cluster exhibits two non-symmetric radio relics well studied through
recent, deep radio data. Our analysis is based on redshift data for 125
galaxies acquired at the Telescopio Nazionale Galileo and on new photometric
data acquired at the Isaac Newton Telescope. We also use ROSAT/HRI archival
X-ray data. We combine galaxy velocities and positions to select 98 cluster
galaxies and analyze the internal dynamics of the cluster. We estimate a mean
redshift <z>=0.1789 and a LOS velocity dispersion \sigma ~ 1070 km/s. The
two-dimensional galaxy distribution reveals the presence of three significant
peaks within a region of ~ 1 Mpc (the E, NW, and SW peaks). The spectroscopic
catalog confirms the presence of these three clumps. The total mass of the
cluster is very uncertain: M~ 2 10^15 solar masses. The E clump well coincides
with the main mass peak as recovered from the weak gravitational lensing
analysis and is off-set to the east from the BCG by ~ 1.3 arcmin. The ROSAT
X-ray data also show a very complex structure, mainly elongated in the E-W
direction, with two (likely three) peaks in the surface brightness
distribution, which, however, are off-set from the position of the peaks in the
galaxy density. The observed phenomenology agrees with the hypothesis that we
are looking at a complex cluster merger occurring along two directions: a major
merger along the ~ E-W direction (having a component along the LOS) and a minor
merger in the western cluster regions along the ~ N-S direction, roughly
parallel to the plane of the sky.
