Correlation effects described by the displacement–displacement correlation function [Formula: see text] have been studied based on Debye–Waller factors presented by the mean square displacement (MSD) [Formula: see text] and mean square relative displacement (MSRD) [Formula: see text] in X-ray Absorption Fine Structure. Analytical expressions have been derived for [Formula: see text] based on the anharmonic correlated Debye model (ACDM) and for [Formula: see text] based on anharmonic Debye model (ADM) or uncorrelated Debye model. Many-body effects have been taken into account in the present one-dimensional model by a simple measure based on the anharmonic effective potentials that include interactions of absorber and backscatterer atoms with their nearest neighbors. Morse potential is used for describing single-pair atomic interaction. The reasons for the difference between MSRD and MSD have been discussed in detail. The theory is applied to fcc crystals and can be generalized to any crystal structure. Numerical results for Cu are found to be in good agreement with the experimental values and with those taken from the measured Morse parameters, as well as with the values of [Formula: see text] calculated using the other theories.