In designing structures to withstand earthquakes, the engineer is mainly concerned with relatively strong motions, in which source dimensions and non-linear effects become important. A model for the attenuation of strong, near-field motions is used to assess the parameters of Scandinavian earthquakes. It is concluded that the Scandinavian earthquakes may be attenuated more slowly and have higher maximum accelerations and higher frequencies some distance away from the source than earthquakes in western U.S.A. for the same magnitude.