  Using a dynamical 3-D reconstruction procedure we estimate the peculiar
velocities of $R\ge0$ Abell/ACO galaxy clusters from their measured redshift
within 25000 km/sec. The reconstruction algorithm relies on the linear
gravitational instability hypothesis, assumes linear biasing and requires an
input value of the cluster $\beta$-parameter ($\beta_c \equiv
\Omega_{\circ}^{0.6}/b_c$), which we estimated in Branchini \& Plionis (1995)
to be $\beta_c\simeq 0.21$. The resulting cluster velocity field is dominated
by a large scale streaming motion along the Perseus Pisces--Great Attractor
base-line directed towards the Shapley concentration, in qualitative agreement
with the galaxy velocity field on smaller scales. Fitting the predicted cluster
peculiar velocities to a dipole term, in the local group frame and within a
distance of $\sim 18000$ km/sec, we recover extremely well both the local group
velocity and direction, in disagreement with the Lauer \& Postman (1994)
observation. However, we find a $\sim 6\%$ probability that their observed
velocity field could be a realization of our corresponding one, if the latter
is convolved with their large distance dependent errors. Our predicted cluster
bulk velocity amplitude agrees well with that deduced by the POTENT and the da
Costa et al. (1995) analyses of observed galaxy motions at $\sim 5000 - 6000$
km/sec; it decreases thereafter while at the Lauer \& Postman limiting depth
($\sim 15000$ km/sec) its amplitude is $\sim 150$ km/sec, in comfortable
agreement with most cosmological models.
