The authors address the process of estimating relative permeability curves from data collected during unsteady-state displacement experiments. They introduce B-splines for use as functional representations of relative permeability curves. With B-splines, polynomial splines of any order can be conveniently implemented in the estimation procedure. This feature allows greater flexibility for incorporating inequality constraints into the parameter-estimation process. The authors present a method for choosing an appropriate number of spline partitions for representing permeability curves. The method is based on considerations for obtaining the most accurate estimates of the relative permeability curves. They illustrate the method with both hypothetical and actual experimental data. They demonstrate that serious estimation errors may be encountered when relative permeability curves are represented with functions containing too few parameters - e.g., power-law functions.