Italian strong-motion data were used to study attenuation characteristics of horizontal peak ground acceleration and velocity. The data base consisted of 190 horizontal components of accelerograms recorded in Italy since 1976 from 17 earthquakes of magnitudes 4.6 to 6.8. The resulting equations are
where A is peak horizontal acceleration in g, V is peak horizontal velocity in centimeters/second, M is magnitude, R is the closest distance to the surface projection of the fault rupture in kilometers, and S is a variable taking the values of 0 and 1 according to the local site geology. Peak acceleration and velocity were found to be lognormally distributed with a standard error representing, respectively, a 49 and 64 per cent increase in the median estimate. We considered a magnitude-dependent shape of the attenuation curves, but we found no basis for it in the data. Attenuation relationships developed using epicentral distance in place of fault distance gave similar results, with higher standard errors and higher predicted values for short distances and high magnitudes. Sensitivity studies, performed with the analysis of the residuals, showed that predictions based on our relatiaons are stable with respect to reasonable variations of the model and the seismic areas providing the data. Comparisons with attenuation relationships proposed for western North America showed differences of the same order of magnitude as the statistical prediction uncertainty.