The relationship between surface wave magnitude, Ms, and seismic moment, M0, of earthquakes is essential for the estimation of seismic risk in any region. In the hypothesis of constant stress drop, theoretical models predict that Log M0 and Ms are related by a linear law. The slope most commonly found in the literature is around 1.5. Here we show that the application to the Ms values of the necessary correlation for the focal depth, gives a general increment of the correlation coefficient, and that a slope around 1.0 is consistent with the global data, while for regionalized data it can vary from about 1.0 to 2.0. ¿ American Geophysical Union 1995