We present an analysis of the two-point correlation function, ξ (r), of the X-ray Brightest Abell-type Cluster sample (XBACs) of Ebeling et al. and of the cosmological constraints that it provides. If ξ (r) is modelled as a power-law, ξ (r)=(r0/r)γ, we find r0 ≃ 26.0 ± 4.5 h−1 Mpc and γ≃ 2.0 ± 0.4, with errors corresponding to 2σ uncertainties for one significant fitting parameter. As a general feature, ξ (r) is found to remain positive up to r ≃ 50–55 h−1 Mpc, after which it declines and crosses zero. Only a marginal increase of the correlation amplitude is found as the flux limit is increased from 5 × 10−12 to 12 × 10−12 erg s−1 cm−2, thus indicating a weak dependence of the correlation amplitude on the cluster X-ray luminosity. Furthermore, we present a method to predict correlation functions for flux-limited X-ray cluster samples from cosmological models. The method is based on the analytical recipe by Mo & White and on an empirical approach to convert cluster fluxes into masses. We use a maximum likelihood method to place constraints on the model parameter space from the XBACs ξ (r). For scale-free primordial spectra, we find that the shape parameter of the power spectrum is determined to lie in the 2σ range 0.05 ≲Γ≲ 0.20. As for the amplitude of the power spectrum, we find σ8≃ 0.4–0.8 for Ω0=1 and σ8≃ 0.8–2.0 for Ω0=0.3. The latter result is in complete agreement with, although less constraining than, results based on the local cluster abundance.