This work is devoted to the study of the dipole structure in the distr
ibution of galaxy clusters and to the constraints that it gives on dar
k-matter models. We use simulations of the cluster distribution, based
on the Zel'dovich approximation, starting from different dark - matte
r models. The aim of our analysis is to check to what extent the obser
ved structure of the cluster dipole represents a constraint for DM mod
els. Our main results can be summarised as follows. Local Group like o
bservers are likely produced in Omega(0)=1 models, quite irrespectivel
y of the detailed power-spectrum shape, while they are more rare in th
e Omega(0)=0.2 CDM models. Misalignment between the directions of the
CMB and cluster dipoles like that observed occurs quite often, althoug
h an accurate alignment is not always guaranteed. About 30%, 40% of th
e observers measure a misalignment below 20 degrees. The observed clus
ter dipole amplitude is more typical in the four high-density (Omega(0
)=1) models than in the low-density (Omega(0)=0.2) ones. Independent e
stimates of the cluster biasing factor in the simulations allows to wo
rk out the value of Omega(0) from cluster dipoles. It turns out that t
he input value (Omega(0)=1 or 0.2) is recovered quite well, thus suppo
rting the reliability of cluster dipole to measure the average matter
density in the Universe.