An analysis is developed for two-component systems in a modified steady-state condition which may be attained in the ultracentrifuge. The method depends on the sharpening effect which generally occurs across a moving boundary, because sedimentation coefficients increase with dilution; this effect is counteracted by diffusion and, accordingly, the sharpening and spreading effects may be made to balance by proper selection of the experimental conditions. Owing to radial dilution and the inhomogeneous field, a true steady state cannot occur, but certain characteristics of the boundary do become independent of time. With multi-component systems which yield a single boundary, the diffusional spreading is augmented by the effect of heterogeneity: thus a steady state, if attainable, can occur only when the gravitational field is increased to balance this effect also. When such systems are analysed in terms of the equations valid for two-component systems, the deviations from homogeneity are manifested as a difference between the apparent diffusion coefficient (i.e. the spreading coefficient) and the true diffusion coefficient. The analysis has been tested by application to a purified protein and a polydisperse mucopolysaccharide. It is shown that an approximately steady state is readily attainable under certain experimental conditions, and that the method provides a sensitive means of detecting impurities and characterizing heterogeneity, although the 2-component analysis is not adequate to interpret fully the behaviour of very polydisperse systems.