  We investigate the feasibility of carrying out likelihood analysis on the
velocities of galaxy clusters to determine power spectrum parameters. Using
N-body simulations of cosmological density fields we show that the velocity
field traced by clusters is highly non-linear on small scales (r < 10 h^-1
Mpc), mostly due to strong infall into superclusters. The transverse and line
of sight velocity correlation functions relevant to likelihood analysis deviate
significantly from the linear theory values. Unfortunately, the sparseness of
cluster samples means that they are not amenable to any rigorous smoothing
procedure to rectify this. We are forced instead to remove close pairs of
clusters which would contribute disproportionately to the likelihood. This
reduces the size still further of the small samples of observed clusters
available to us, forcing us into the conclusion that using straightfoward
linear theory covariance analysis on clusters is unpromising. Nevertheless we
apply the technique to two sets of observational data and find marginal
evidence for more power in the mass density field than standard CDM. The
normalisation is consistent with \Omega^{0.6}\sigma_{8} \sim 0.7 for both data
sets, within the (large) errors.
