  (abridged) We use a theoretical model to predict the clustering properties of
galaxy clusters. Our technique accounts for past light-cone effects on the
observed clustering and follows the non-linear evolution of the dark matter
correlation function and cluster bias factor. A linear treatment of
redshift-space distortions is also included. We perform a maximum-likelihood
analysis by comparing the theoretical predictions to a set of observational
data, both in the optical (APM and EDCC catalogues) and X-ray band (RASS1
Bright Sample, BCS, XBACs, REFLEX). In the framework of CDM models, we compute
the constraints on cosmological parameters. Our results show that X-ray data
are more powerful than optical ones, allowing smaller regions in the parameter
space. We find that the clustering properties of clusters are almost
independent of the matter density parameter and of the presence of a
cosmological constant, while they appear to be strongly dependent on the shape
parameter. Using the X-ray data only, we obtain Gamma~0.1 and 0.4<sigma_8<1.1
for the Einstein-de Sitter model, while 0.14<Gamma<0.22 and 0.6<sigma_8<1.3 for
open and flat models with Omega_0m=0.3. Finally, we use our model to make
predictions on the correlation length of galaxy clusters expected in future
surveys. In particular, we show the results for an optical catalogue with
characteristics similar to the EIS project and for a very deep X-ray catalogue
with the characteristics of the XMM/LSS survey. We find that clusters at high
redshifts are expected to have larger a correlation length than local ones.
