Inelastic processes in extended x-ray-absorption fine structure (EXAFS) are studied using an extension of the semiclassical model of dynamical screening of a core hole and a photoelectron. This treatment effectively includes both extrinsic and intrinsic inelastic losses, as well as interference between them. The local-density approximation is used to derive a complex, energy-dependent final-state potential which includes dynamical corrections to the static exchange-correlation potential. A local relaxation method is developed to calculate the core-hole Green's function, from which the EXAFS amplitude-reduction factor can be determined. Applications to EXAFS amplitudes for the diatomic molecule ${\mathrm{Br}}_{2}$ and for metallic Cu yield results in reasonable agreement with experiment.