A thermodynamic method for measuring the acoustic nonlinearity parameterB/Ain tissues is presented. It is based on the measurement of change in phase velocity as a function of time as the hydrostatic pressure of the sample is quickly reduced from a known value. This technique circumvents the effect of the attenuation in the medium and does not require a prior knowledge of the thermodynamic parameters of the tissues. The method is used to estimate nonlinearity parameters for normal and malignant tissues in the temperature range 20° to 37 °C. The values and the temperature dependence of these parameters are found to vary with the nature of the tissues.