The conditions for convection-free band sedimentation are analyzed in terms of the uegative density gradients associated with the leading edge of a band and the positive density gradients generated during the experiment. The amount of material necessary to perform a band-centrifugation experiment depends on the &sion coefficient of the macromolecules, which determines the rate a t which the concentration a t band maximum decreases, and on the extinction coefficient a t the wavelength of observation. The maximum negative gradients in bands of macromolecules with diffusion and extinction coefficients typical of proteins, nucleic acids, and viruses are calculated. Positive density gradients generated by diffusion of small molecules between the thin lamella and the bulk solution are calculated for bulk solutions such as 1M NaCl or 95% D20. These "diffusion gradients" are generally adequate to stabilize bands of the above macromolecules. Positive density gradients generated by sedimentation of salts within the bulk solution may be significant in providing stability near the bottom of the cell. The effects of inadequate stabilizing gradients are discussed, and are found to cause forward spreading of the band. * Contribution No. 3224.