A previous analysis of dual-energy imaging is extended to incorporate scattered radiation. The analysis is general and can include polyenergetic beams and nonideal detectors. In the dual-material basis plane, scatter generates a displacement of the vectors representing the imaged materials. This changes the target versus background signal difference and the projection angle for cancellation of background contrast due to varying amounts of two materials. Complete cancellation is not possible, because vectors representing various mixtures of the two background constituents are displaced differently and thus no longer lie on a straight line in the dual-material plane. The effect can be minimized by allowing a typical amount of scatter to reach the image receptor when determining the parameters of the transformation from log attenuation to equivalent materials thicknesses. The analysis has been applied to dual-energy mammography. The presence of scatter has minimal effect on the optimum beam energies with an ideal detector, which are about 20 and 70 keV.