Ultrasound signals reflected from the human liver contain significant information about its condition. Several techniques have been developed to process such signals. In this paper, two approaches are described for estimating the slope of the acoustic attenuation coefficient, denoted by β, which provides important cues about the condition of diffuse liver disease. The first is a nonparametric approach which determines the β value from the slope of log periodogram differences. The second is a parametric approach which requires a Gaussian-shaped spectrum and determines the β value from s shift in the spectral center-frequency. A zero-crossing count procedure allows the parametric approach to be implemented with minimal hardware and in real-time. Simulated and actual signals illustrate the two approaches.