An investigation of the frequency evolution of the quality factor in Gaussian media is conducted. By means of a source with a restricted spectrum, a method is developed to measure accurate values of Q-1. When the fluctuations of the velocity are less than 4%, it is shown that the results are in good agreement with the formula of Wu. However, it is noticed that for such media the attenuation is too weak to be measured in a real seismic survey. It is shown that codas and the attenuation of the first arrival are closely related. The evolution of the function Q-1(f) is studied for large fluctuations in the nonlinear range. ¿American Geophysical Union 1991