A new theory of nonspecular x-ray scattering from layered systems with random rough interfaces based on the distorted-wave Born approximation is presented. Calculations of the diffuse scattering from a single gold layer and two W/Si multilayer mirrors has been carried out. The theory explains the existence of maxima and minima in the angular distribution of diffusely scattered intensity resulting from standing-wave-enhanced scattering and other dynamical effects. The influence of the mutual correlation between individual interface profiles on x-ray scattering is discussed. © 1995 American Institute of Physics.