Basis material decomposition represents dual‐energy x‐ray attenuation measurements in terms of the attenuation coefficients or thicknesses of two standard materials which, when combined, produce attenuation equivalent to the object being measured. In tomographic imaging, the reconstructed attenuation coefficient is calculated in terms of the attenuation coefficients of the basis materials, while in projection imaging, the thicknesses of two materials can be specified in terms of the basis materials. This analysis shows that basis material decomposition is exact in a dual‐monoenergetic system, but for broad spectra, x‐ray beam hardening introduces a bias into quantitative measurements. The error is small enough that it can be ignored when dual‐energy imaging is used primarily to enhance the contrast of one material over another. The magnitude of the error in quantitative measurements depends on the details of the specific application including the energy of the x‐ray beam, and the composition and thickness of the materials included in the object. The magnitude of the error for dual‐energy bone densitometry has been analyzed using a first‐order propagation of error analysis and the calculations verified by computer simulation. This analysis shows that the magnitude of the systematic error can be as high as 3% for 1 g/cm2of bone mineral when aluminum and acrylic basis materials are used for the calibration. This systematic error is eliminated when the basis materials are the same as the materials that are being quantified (i.e., bone mineral and water).