Ultrasonic velocity and attenuation measurements were made on dry, brine- and oil-saturared Berea sandstone and fused glass beads. The results for fused glass beads are consistent with the predictions of Biot theory. They indicate that as predicted, the Biot absorption/dispersion mechanism shifts to higher frequencies as the fluid viscosity increases. Similar data for Berea sandstone are not consistent with Biot theory, since observed velocities are generally higher than predicted. Using the Biot theory, we calculate low- and high-frequency velocities for the liquid-saturated samples. ''Biot dispersion'' is then defined as the precent difference between the low- and high-frequency limits. ''Apparent dispersion'' is defined as the percent difference between the measured ultrasonic velocity and the low-frequency Biot limit. Comparison of these two measures of dispersion gives insight into the presence of a non-Biot absorption/dispersion mechanism. Whenever the apparent dispersion is larger than the Biot dispersion, the extra dispersion is interpreted as being caused by a local flow relaxation. To be consistent with attenuation data, this relaxation must be distributed over at least five to six decades in frequency.