Percolation theory is used in this paper to study the general accessibility characteristics of bond site correlated networks in the presence or absence of spatial correlations among the sites. Spectral methods are employed to generate networks in which the sites are spatially correlated according to exponential or Gaussian autocovariance functions. Monte Carlo simulations are performed for bond-correlated site percolation with and without trapping, as related to drainage-type displacements of water by oil (or air) and air by mercury, respectively. For the correlation modes studied, it is found that spatial correlations result in significant reduction of the site percolation threshold with a concomitant modification of the site accessibility. However, the bond accessibility characteristics and the bond percolation threshold are not significantly affected. The simulated drainage capillary pressure curves become more gradual and the residual wetting phase saturation associated with oil (or air)-water displacements is significantly decreased when spatial correlations among the pore bodies exist. ¿ American Geophysical Union 1993